File:Julia set for f(z) = z^2 + i using BDM DEM LSM.png
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Julia set for f(z) = z^2 + i using BDM DEM LSM
Summary
[edit]_%3D_z%5E2_%2B_i_using_BDM_DEM_LSM.png&action=edit§ion=1){kind=link}
| Description |
English: Julia set for f(z) = z^2 + i using BDM DEM LSM |
| Date | |
| Source | Own work |
| Author | Soul windsurfer |
c source code
[edit]_%3D_z%5E2_%2B_i_using_BDM_DEM_LSM.png&action=edit§ion=2){kind=link}
/*
Numerical approximation of Julia set for fc(z)= z^2 + c
Adam Majewski
adammaj1 aaattt o2 dot pl // o like oxygen not 0 like zero
--------------------------------------------------------------------
Structure of a program or how to analyze the program
DrawImageOf -> DrawPointOf -> ComputeColorOf ( FunctionTypeT FunctionType , complex double z) -> ComputeColor
check only last function which computes color of one pixel for given Function Type
==========================================
---------------------------------
indent d.c
default is gnu style
-------------------
c console progam
export OMP_DISPLAY_ENV="TRUE"
gcc n.c -lm -Wall -march=native -fopenmp
time ./a.out > j.txt
gcc n.c -lm -Wall -march=native -fopenmp
time ./a.out
time ./a.out >i.txt
time ./a.out >e.txt
make
convert -limit memory 1000mb -limit disk 1gb dd30010000_20_3_0.90.pgm -resize 2000x2000 10.png
*/
#include <stdio.h>
#include <stdlib.h> // malloc
#include <string.h> // strcat
#include <math.h> // M_PI; needs -lm also
#include <complex.h>
#include <omp.h> // OpenMP
#include <limits.h> // Maximum value for an unsigned long long int
// https://sourceforge.net/p/predef/wiki/Standards/
#if defined(__STDC__)
#define PREDEF_STANDARD_C_1989
#if defined(__STDC_VERSION__)
#if (__STDC_VERSION__ >= 199409L)
#define PREDEF_STANDARD_C_1994
#endif
#if (__STDC_VERSION__ >= 199901L)
#define PREDEF_STANDARD_C_1999
#endif
#endif
#endif
/* --------------------------------- global variables and consts ------------------------------------------------------------ */
#define PROGRAM_VERSION 20230409
int NumberOfImages = 0;
// virtual 2D array and integer ( screen) coordinate
// Indexes of array starts from 0 not 1
//unsigned int ix, iy; // var
static unsigned int iHeight = 8000; //
static unsigned int iyMin = 0; // Indexes of array starts from 0 not 1
static unsigned int iyMax; //
static unsigned int ixMin = 0; // Indexes of array starts from 0 not 1
static unsigned int ixMax; //
static unsigned int iWidth; // horizontal dimension of array
// The size of array has to be a positive constant integer
static unsigned long long int iSize; // = iWidth*iHeight;
// memmory 1D array for 8 bit color
unsigned char *data;
unsigned char *edge;
unsigned char *edge2;
//unsigned char *edge2;
// rgb array = 24bit color = 3 bytes
int iColorSize = 3 ; // RGB = 3*(unsigned char)
unsigned int iSize_rgb; // number of elements in rgb array
unsigned char *rgbData;
// unsigned int i; // var = index of 1D array
//static unsigned int iMin = 0; // Indexes of array starts from 0 not 1
unsigned int iMax; // = i2Dsize-1 =
// The size of array has to be a positive constant integer
// unsigned int i1Dsize ; // = i2Dsize = (iMax -iMin + 1) = ; 1D array with the same size as 2D array
//FunctionType = representing functions
typedef enum {FatouBasins = 0, FatouComponents = 2, LSM = 3, LSM_m = 4, Unknown = 5 , BDM = 6, MBD = 7 , MBD2 = 8, SAC = 9, DLD = 10, ND = 11, NP= 12, POT = 13 , Blend = 14, DEM = 15
} FunctionTypeT;
/*
type you want to achieve or intent type
for dendrite type c must be
- Misiurewicz point
- Generalized Feigenbaum point: the limit of the period-q cascade of bifurcations and landing points of parameter ray or rays with irrational angles )
- others which have no description
*/
typedef enum {superattracting = 100, attracting = 200, parabolic = 300, repelling = 400, dendrite = 500, siegel = 600
} DynamicTypeT;
DynamicTypeT DynamicType; // it is set manually
// see ComputeColor_FunctionType_DynamicType belwo
// see SetPlane
double radius = 1.2;
complex double center = 0.0 ;
double DisplayAspectRatio = 1.0; // https://en.wikipedia.org/wiki/Aspect_ratio_(image)
// dx = dy compare setup : iWidth = iHeight;
double ZxMin; //= -1.3; //-0.05;
double ZxMax;// = 1.3; //0.75;
double ZyMin;// = -1.3; //-0.1;
double ZyMax;// = 1.3; //0.7;
double PixelWidth; // =(ZxMax-ZxMin)/ixMax;
double PixelHeight; // =(ZyMax-ZyMin)/iyMax;
// dem
double BoundaryWidth; // = 1.0*iWidth/2000.0; // measured in pixels ( when iWidth = 2000)
double distanceMax ; //= BoundaryWidth*PixelWidth;
double ratio;
double ER;
double ER2; //= 1e60;
double AR; // bigger values do not works
double AR2;
double R_BDM;
double R2_BDM;
complex double parabolic_trap_center;
double PixelWidth2;
int IterMax = pow(10,7);
int IterMax_LSM = pow(10,7);
int IterMax_BDM = pow(10,9);
int IterMax_DEM = 10000000;
/* colors = shades of gray from 0 to 255 */
unsigned char iColorOfBasin1 = 170;
unsigned char iColorOfInterior = 150;
unsigned char iColorOfExterior = 225;
unsigned char iColorOfBoundary = 0;
unsigned char iColorOfUnknown = 5;
// pixel counters; pixel counters work not good with OpenMP !!!
unsigned long long int uUnknown = 0;
unsigned long long int uInterior = 0;
unsigned long long int uExterior = 0;
const int period = 1;
const int period_parent = 1;
const int period_child = 11;
const int t_numerator = 5;
int t_denominator = period_child;
double t0; // for MBD https://www.youtube.com/watch?v=JttLtB0Gkdk&t=894s
double t2 = 0.435;
/* critical point */
complex double zcr = 0.0; //
// c = 0.397391822296541 +0.133511204871878 i period = 0
complex double c = I; // 1/6
// 1 superattracting cycle period 1
double delta; // delta is a distance between fixed points
/*
alfa < 1/2 <beta
cabs(beta - alfa) = delta
alfa = ( 1 - delta)/2
beta = ( 1 + delta)/2
delta = sqrt(1- 4c)
*/
complex double zp = 0.0; // one of periodic pointes , alfa
complex double zcr_last = 0.397391822296541 +0.133511204871878*I ; // t = 129 /16256
/*
for parabolic triangle trap ( computed in other program: last point of first and last ray ( ordered by t )
Maximal number of iterations = iterMax_ray = 2000000000000
p = 0 t = 0.1665852467024914 z = -0.4170188752901364 +0.1506018053351233*I distance to landing point = 0.0634786084515321 = 70.4965212747848113* PixelWidth = 0.0352658935841845*ImageWidth
p = 1 t = 0.3331704934049829 z = -0.5388360314336247 +0.1504188918297714*I distance to landing point = 0.0598567181450451 = 66.4742108733029085* PixelWidth = 0.0332537323028029*ImageWidth
p = 2 t = 0.6663409868099658 z = -0.4223414442666910 +0.1139242453319452*I distance to landing point = 0.0634130274946685 = 70.4236899788012778* PixelWidth = 0.0352294597192603*ImageWidth
Maximal number of iterations = iterMax_ray = 20000
p = 0 t = 0.1665852467024914 z = -0.3350594976618946 +0.1652825185133397*I distance to landing point = 0.1467326739625789 = 162.9547862506640570* PixelWidth = 0.0815181522014327*ImageWidth
p = 1 t = 0.3331704934049829 z = -0.6051132306923424 +0.1652675081250403*I distance to landing point = 0.1277193817845747 = 141.8394689929804144* PixelWidth = 0.0709552121025415*ImageWidth
p = 2 t = 0.6663409868099658 z = -0.3512112430996852 +0.0760154138719138*I distance to landing point = 0.1439685504118509 = 159.8850734851610866* PixelWidth = 0.0799825280065838*ImageWidth
z2 = parabolic fixed point
triangle trap for components are different ( bigger) then triangle trap for BDM !!!!
triangle (z1,zp,z3)
z1
zp zcr_last
z3
*/
complex double z1 = -0.3350594976618946 +0.1652825185133397*I ; //-0.4170188752901364 +0.1506018053351233*I ;
complex double z3 = -0.3512112430996852 +0.0760154138719138*I ; // -0.4223414442666910 +0.1139242453319452*I;
complex double z13;
// for MBD
static double TwoPi=2.0*M_PI; // texture
//double t0 ; // t for MBD
// see https://www.youtube.com/watch?v=JttLtB0Gkdk&t=894s
//
// update with f function
const char *f_description = "Numerical approximation of Julia set for f(z)= z^2 + c "; // without /n !!!
/* ------------------------------------------ functions -------------------------------------------------------------*/
// complex function
// upadte f_description also
complex double f(const complex double z0) {
double complex z = z0;
z = z*z + c;
return z;
}
complex double derivative_wrt_z(const complex double z0) {
double complex z = z0;
z = 2.0*z ;
return z;
}
double c_arg(complex double z)
{
double arg;
arg = carg(z);
if (arg<0.0) arg+= TwoPi ;
return arg;
}
double c_turn(complex double z)
{
double arg;
arg = c_arg(z);
return arg/TwoPi;
}
double cabs2(complex double z){
return creal(z)*creal(z)+cimag(z)*cimag(z);
}
// Distance Estimation Method for Julia set ( DEM/J ) estimates distance from point z ( in the exterior of Julia set ) to nearest point in Julia set.
double compute_distance(const complex double z0){
int nMax = IterMax_DEM;
complex double z = z0;
complex double dz = 1.0; // is first derivative with respect to z
double distance;
double cabsz;
int n;
for (n=0; n < nMax; n++){ //forward iteration
if (cabs2(z)> ER2 || cabs(dz)> 1e60) break; // big values
dz = derivative_wrt_z(z) * dz;
z = f(z); /* forward iteration : complex quadratic polynomial */
}
if (n==nMax) return -1.0; // not escaping
// escaping and boundary
cabsz = cabs(z);
distance = 2.0 * cabsz* log(cabsz)/ cabs(dz);
return distance;
}
int is_z_outside(complex double z){
if (creal(z) >ZxMax ||
creal(z) <ZxMin ||
cimag(z) >ZyMax ||
cimag(z) <ZyMin)
{return 1; } // is outside = true
return 0; // is inside = false
}
complex double GiveFixed(complex double c){
/*
Equation defining fixed points : z^2-z+c = 0
z*2+c = z
z^2-z+c = 0
coefficients of standard form ax^2+ bx + c
a = 1 , b = -1 , c = c
The discriminant d is
d=b^2- 4ac
d = 1 - 4c
alfa = (1-sqrt(d))/2
*/
complex double d = 1-4*c;
complex double z = (1-csqrt(d))/2.0;
return z;
}
// from screen to world coordinate ; linear mapping
// uses global cons
double GiveZx (int ix)
{
return (ZxMin + ix * PixelWidth);
}
// uses globaal cons
double GiveZy (int iy)
{
return (ZyMax - iy * PixelHeight);
} // reverse y axis
complex double GiveZ (int ix, int iy)
{
double Zx = GiveZx (ix);
double Zy = GiveZy (iy);
return Zx + Zy * I;
}
// -------------------- parabolic triangle trap =----------------------------------------------------------
// ---------------------------------------------------------------------------------------------------------
double IsTriangleCounterclockwise(double xa, double ya, double xb, double yb, double xc, double yc)
{return ((xb*yc + xa*yb +ya*xc) - (ya*xb +yb*xc + xa*yc)); }
int DescribeTriangle(double xa, double ya, double xb, double yb, double xc, double yc)
{
double t = IsTriangleCounterclockwise( xa, ya, xb, yb, xc, yc);
if (t>0) printf("this triangle is oriented counterclockwise, determinent = %f \n", t);
if (t<0) printf("this triangle is oriented clockwise, determinent = %f\n", t);
if (t==0) printf("this triangle is degenerate: colinear or identical points, determinent = %f\n", t);
return 0;
}
int Describe_Triangle(const double complex z1, const double complex z2, const double complex z3){
return DescribeTriangle( creal(z1), cimag(z1), creal(z2), cimag(z2), creal(z3), cimag(z3));
}
// http://stackoverflow.com/questions/2049582/how-to-determine-a-point-in-a-2d-triangle
// In general, the simplest (and quite optimal) algorithm is checking on which side of the half-plane created by the edges the point is.
double side (double x1, double y1, double x2,double y2,double x3, double y3)
{
return (x1 - x3) * (y2 - y3) - (x2 - x3) * (y1 - y3);
}
// the triangle node numbering is counter-clockwise / clockwise
int PointInTriangle (double x, double y, double x1, double y1, double x2, double y2, double x3, double y3)
{
int b1, b2, b3;
b1 = side(x, y, x1, y1, x2, y2) < 0.0;
b2 = side(x, y, x2, y2, x3, y3) < 0.0;
b3 = side(x, y, x3, y3, x1, y1) < 0.0;
return ((b1 == b2) && (b2 == b3));
}
/*
z1
zp zcr_last
z3
*/
// uses global var: z1, zp, z3 describing triangle(z1, zp, z3)
int IsPointIn_Parabolic_Components_Triangle(const double complex z){
return PointInTriangle (creal(z), cimag(z), creal(z1), cimag(z1), creal(zp), cimag(zp), creal(z3), cimag(z3));
}
/* divide circle around critical point into 4 equal segments , manual tuning
t0 = 5/11
tn = n/4
t0+1/4 0.18 0.175 0.1786329062544335
0.0 0.0 0.0
1.0*2/4 1*3/4 0.43 0.93 0.425 0.925 0.4286329062544335 0.9286329062544335
1* 0.7 0.675 0.6786329062544335
z = -0.0559603266109820 -0.1163177312664140
t1 = 0.1786329062544335 = t2 - 0.25
t2 = 0.4286329062544335 = t3 - 0.25 ** 0.429 0.44 ( tu much ) 0.435
t3 = 0.6786329062544335 = c_turn(z)
t4 = 0.9286329062544335 = t3 + 0.25 **0.929
t2 - t1 = 0.2500000000000000
t3 - t2 = 0.2500000000000000
t4 - t3 = 0.2500000000000000
t1+ (1.0 - t4) = 0.2500000000000001
*/
int IsPointIn_BDM_TriangleB(const double complex z){
int b = PointInTriangle (creal(z), cimag(z), creal(z1), cimag(z1), creal(zp), cimag(zp), creal(zcr_last), cimag(zcr_last));
int bm = PointInTriangle (creal(z), cimag(z), creal(-z1), cimag(-z1), creal(-zp), cimag(-zp), creal(-zcr_last), cimag(-zcr_last));
int c = 0;
if (cabs2(z) < R2_BDM ){
double turn = c_turn(z);
//c = ((turn > 0.75 + t0 && turn < 0 + t0) || (turn > 0.25 + t0 && turn < 0.5 + t0)); // divide circle into 4 equal segments rotated by t0
c = ((turn > 0.1786 && turn < t2) || (turn > 0.6786 && turn < 0.935 )); // divide circle into 4 equal segments rotated by t0 }
}
return (b || bm || c);
}
/*
z1
zp zcr_last
z3
*/
int IsPointIn_BDM_TriangleA(const double complex z){
int a = PointInTriangle (creal(z), cimag(z), creal(zcr_last), cimag(zcr_last), creal(zp), cimag(zp), creal(z3), cimag(z3));
int am = PointInTriangle (creal(z), cimag(z), creal(-zcr_last), cimag(-zcr_last), creal(-zp), cimag(-zp), creal(-z3), cimag(-z3));
int c = 0;
if (cabs2(z) < R2_BDM ){
double turn = c_turn(z);
//c = ((turn > 0.5 + t0 && turn < 0.75 + t0) || (turn > 0 + t0 && turn < 0.25 + t0)); // divide circle into 4 equal segments rotated by t0
c = ((turn > 0.935 || turn < 0.1786) || (turn > t2 && turn < 0.6786)); // divide circle into 4 equal segments rotated by t0
}
return (a || am || c);
}
//------------------complex numbers -----------------------------------------------------
/* ----------- array functions = drawing -------------- */
/* gives position of 2D point (ix,iy) in 1D array ; uses also global variable iWidth */
unsigned int Give_i (unsigned int ix, unsigned int iy)
{
return ix + iy * iWidth;
}
// ****************** DYNAMICS = trap tests ( target sets) ****************************
// circular trap with zp as a center
int IsInsideTrap(int ix, int iy){
complex double z = GiveZ(ix, iy);
if ( cabs2(z - zp) < AR2 )
{return 1;}
return 0;
}
/*
************************************************** ComputeColor_FunctionType_DynamicType *********************************************
Make ComputeColor_FunctionType_DynamicType function for each combination of 2 enums
* FunctionTypeT
* DynamicTypeT
then update Compute8BitColor procedure :
case FunctionType + DynamicType: {ComputeColor_FunctionType_DynamicType(z); break;}
run procedure inside MakeImages using DrawImage (array, FunctionType);
second enum DynamicType is updated manually inside main function
********************************************************************************************************************************************
*/
// ********************************************************************************************************************
/* ---------------------FatouBasins -----------------------------------------------------------*/
// ********************************************************************************************************************
/*
2 basins, both superattracting
- exterior
- interior
- unknown ( possibly empty set )
pixel counters work not good with OpenMP !!!
*/
unsigned char ComputeColor_FatouBasins_superattracting (complex double z)
{
double cabs2z;
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// 2 basins, both superattracting
cabs2z = cabs2(z);
// infinity is superattracting here !!!!!
if ( cabs2z > ER2 ){ return iColorOfExterior;}
// second superAttraction basins. Here one of superattracting point is zp= 0
if ( cabs2z < AR2 ){ uInterior += 1;return iColorOfInterior;}
z = f(z); // iteration: z(n+1) = f(zn)
}
return iColorOfUnknown;
}
/*
2 basins
- exterior
- interior
- unknown ( possibly empty set )
pixel counters work not good with OpenMP !!!
*/
unsigned char ComputeColor_FatouBasins_attracting (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
// infinity is superattracting here !!!!!
if ( cabs2(z) > ER2 ){ uExterior +=1; return iColorOfExterior;}
// 1 Attraction basins: attracting point zp is not equall to zero
if ( cabs2(zp-z) < AR2 ){ uInterior += 1; return iColorOfInterior;}
z = f(z); // iteration: z(n+1) = f(zn)
}
uUnknown += 1;
return iColorOfUnknown;
}
// basin works bad for parabolic
unsigned char ComputeColor_FatouBasins_parabolic (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// infinity is superattracting here !!!!!
if ( cabs2(z) > ER2 ){ return iColorOfExterior;}
// parabolic basins
if ( cabs2(zp-z) < AR2)
{ uInterior += 1; return iColorOfInterior;}
z = f(z); // iteration: z(n+1) = f(zn)
}
uUnknown += 1;
return iColorOfUnknown;
}
unsigned char ComputeColor_FatouBasins_repelling (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// infinity is superattracting here !!!!!
if ( cabs2(z) > ER2 ){ return iColorOfExterior;}
// no Attraction basins
z = f(z); // iteration: z(n+1) = f(zn)
}
uUnknown += 1;
return iColorOfUnknown;
}
unsigned char ComputeColor_FatouBasins_dendrite (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// infinity is superattracting here !!!!!
if ( cabs2(z) > ER2 ){ return iColorOfExterior;}
// no Attraction basins
z = f(z); // iteration: z(n+1) = f(zn)
}
uUnknown += 1;
return iColorOfUnknown;
}
// ********************************************************************************************************************
/* ---------------------FatouComponents -----------------------------------------------------------*/
// ********************************************************************************************************************
unsigned char ComputeColor_FatouComponents_superattracting (complex double z)
{
double cabs2z;
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
cabs2z = cabs2(z);
// first superAttraction basin : infinity is superattracting for all polynomials
if ( cabs2z > ER2 ){ return iColorOfExterior;}
//second superattraction basins
if ( cabs2z < AR2 ){ return iColorOfBasin1 - (i % period_child)*40;}
z = f(z); // iteration: z(n+1) = f(zn)
}
return iColorOfUnknown;
}
unsigned char ComputeColor_FatouComponents_attracting (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// first basin is superAttraction: infinity is superattracting for all polynomials
if ( cabs2(z) > ER2 ){ return iColorOfExterior;}
//1 Attraction basins
if ( cabs2(zp-z) < AR2 ){ return iColorOfBasin1 - (i % period_child)*20;}
z = f(z); // iteration: z(n+1) = f(zn)
}
return iColorOfUnknown;
}
unsigned char ComputeColor_FatouComponents_parabolic (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// superattracting basin ( infinity is superattracting here )
if ( cabs2(z) > ER2 ){ return iColorOfExterior;}
// parabolic basins
if (IsPointIn_Parabolic_Components_Triangle(z) )
{ return iColorOfBasin1 - (i % period_child)*11;}
z = f(z); // iteration: z(n+1) = f(zn)
}
return iColorOfUnknown;
}
unsigned char ComputeColor_FatouComponents_repelling (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax; ++i)
{
// there is onlt one component = basin of infinity, infinity is superattracting
if ( cabs2(z) > ER2 ){ return iColorOfExterior;}
z = f(z); // iteration: z(n+1) = f(zn)
}
uUnknown += 1;
return iColorOfUnknown;
}
// ********************************************************************************************************************
/* ---------------------Level Set Method = LSM -----------------------------------------------------------*/
// ********************************************************************************************************************
/*
2 basins
exterior is basin of infinity
interior is superattracting
julia set is connected
*/
unsigned char ComputeColor_LSM_superattracting(complex double z)
{
//double cabsz2;
//double distance;
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
double cabs2z = cabs2(z);
// infinity is superattracting here ,
// if ( cabs2z > ER2 ) { return (13*i) % 255;} // exterior
// if ( cabs2z < AR2 ) { return 255- ((7*i) % 255);} // interior
if ( cabs2z > ER2 || ( cabs2z < AR2 ))
{ return (10*i) % 255;} // cabs2(zp-z) = cabs2(z) because zp = zcr = 0
z = f(z);
}
return iColorOfUnknown;
}
/*
2 basins
exterior is basin of infinity
interior is attracting
julia set is connected
*/
unsigned char ComputeColor_LSM_attracting(complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
//double cabs2z = cabs2(z);
// infinity is superattracting here , only one basin
if ( cabs2(z) > ER2 ) { return (13*i) % 255;} //
if ( cabs2(zp - z) < AR2 ) { return 255- ((7*i) % 255);} //
z = f(z);
}
return iColorOfUnknown;
}
/*
for child_period 1 and 2 it can work
for child period > 2 it not works, because target set is a triangle fragment of circle = not works good for parabolic case
z_n < center < z_p
here AR = (z_p - z_n)/2
It is parabolic case: compute AR and change trap center in the local setup procedure
*/
unsigned char ComputeColor_LSM_parabolic(complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
//cabsz = cabs(z);
// infinity is superattracting here !!!!!
if ( cabs2(z) > ER2 )
{ return (10*i) % 255;} // cabs2(zp-z) = cabs2(z) because zp = zcr = 0
//distance = cabs(z - zp);
if (IsPointIn_Parabolic_Components_Triangle(z) ) // if z is inside target set ( orbit trap) = interior of cirlce with radius AR
{ return (10*i) % 255;} //
z = f(z);
}
return iColorOfUnknown;
}
/*
no interior = julia set is disconnected = only one basin here
*/
unsigned char ComputeColor_LSM_repelling(complex double z)
{
//double cabsz2;
//double distance;
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
//cabsz = cabs(z);
// infinity is superattracting here , only one basin
if ( cabs2(z) > ER2 )
{ return (10*i) % 255;} // cabs2(zp-z) = cabs2(z) because zp = zcr = 0
z = f(z);
}
return iColorOfUnknown;
}
/*
no interior = julia set is disconnected = only one basin here
*/
unsigned char ComputeColor_LSM_dendrite(complex double z)
{
//double cabsz2;
//double distance;
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
//cabsz = cabs(z);
// infinity is superattracting here , only one basin
if ( cabs2(z) > ER2 )
{ return (10*i) % 255;} // cabs2(zp-z) = cabs2(z) because zp = zcr = 0
z = f(z);
}
return iColorOfUnknown;
}
// ********************************************************************************************************************
/* ---------------------Binary Decomposition Method = BDM -----------------------------------------------------------*/
// ********************************************************************************************************************
unsigned char ComputeColor_BDM_superattracting (complex double z)
{
double cabs2z;
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
cabs2z = cabs2(z); // numerical speed up : cabs2(zp-z) = cabs2(z) because zp = zcr = 0
// if z is inside target set ( orbit trap) = exterior of circle with radius ER
if ( cabs2z > ER2 || cabs2z < AR2) // exterior
{
if (cimag(z) > 0) // binary decomposition of target set
{ return 0;}
else {return 255; }
}
z = f(z);
}
return iColorOfUnknown;
}
unsigned char ComputeColor_BDM_attracting (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
//cabs2z = ; // numerical speed up : cabs2(zp-z) = cabs2(z) because zp = zcr = 0
// if z is inside target set ( orbit trap) = exterior of circle with radius ER
if ( cabs2(z) > ER2 ) // exterior
{
if (cimag(z) > 0) // binary decomposition of target set
{ return 0;}
else {return 255; }
}
if ( cabs2(zp - z) < AR2 ) // exterior
{
if (cimag(z) > 0) // binary decomposition of target set
{ return 0;}
else {return 255; }
}
z = f(z);
}
return iColorOfUnknown;
}
unsigned char ComputeColor_BDM_parabolic (complex double z)
{
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
// if z is inside target set ( orbit trap) = exterior of circle with radius ER
if ( cabs2(z) > ER2 ) // exterior
{
if (cimag(z) > 0) // binary decomposition of target set
{ return 0;}
else {return 255; }
}
if (IsPointIn_BDM_TriangleB(z))
{ return 100 ; } //50 + (i % period_child);}
if (IsPointIn_BDM_TriangleA(z))
{return 200; } // 255 - (i % period_child); }
z = f(z);
}
return iColorOfUnknown;
}
/*
no interior = julia set is disconnected = only one basin here
*/
unsigned char ComputeColor_BDM_repelling (complex double z)
{
double cabs2z;
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
cabs2z = cabs2(z); // numerical speed up : cabs2(zp-z) = cabs2(z) because zp = zcr = 0
// if z is inside target set ( orbit trap) = exterior of circle with radius ER
if ( cabs2z > ER2 ) // exterior
{
if (cimag(z) > 0) // binary decomposition of target set
{ return 0;}
else {return 255; }
}
z = f(z);
}
return iColorOfUnknown;
}
/*
no interior = julia set is disconnected = only one basin here
*/
unsigned char ComputeColor_BDM_dendrite (complex double z)
{
double cabs2z;
int i; // number of iteration
for (i = 0; i < IterMax_LSM; ++i)
{
cabs2z = cabs2(z); // numerical speed up : cabs2(zp-z) = cabs2(z) because zp = zcr = 0
// if z is inside target set ( orbit trap) = exterior of circle with radius ER
if ( cabs2z > ER2 ) // exterior
{
if (cimag(z) > 0) // binary decomposition of target set
{ return 0;}
else {return 255; }
}
z = f(z);
}
return iColorOfUnknown;
}
// ************************** DEM/J*****************************************
/*
it can be used for
* whole image thru Compute8BitColor function
*/
unsigned char ComputeColorOfDEMJ(complex double z){
// https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Julia_set#DEM.2FJ
unsigned char iColor;
double distance = compute_distance (z); // positive number
if ( distance < 0.0) // not escaping
{ iColor = iColorOfInterior;}
else {
// escaping = exterior and boundary
if (distance < distanceMax ) // boundary
{ double g = tanh(distance); // /PixelWidth); // in [0,tanh(1) = 0.761594] range
iColor = 255*g;}
else iColor = iColorOfExterior; // exterior
}
//if (distance <distanceMax) {//printf(" distance = %f \n", distance);
// return iColorOfBoundary;}
return iColor; // Color of Pixel ( 8 bit ) = shade of gray;
}
/*
==================================================================================================
============================= Draw functions ===============================================================
=====================================================================================================
typedef enum {FatouBasins = 0, FatouComponents = 2, LSM = 3, LSM_m = 4, Unknown = 5 , BDM = 6, MBD = 7 , MBD2 = 8, SAC = 9, DLD = 10, ND = 11, NP= 12, POT = 13 , Blend = 14, DEM = 15} FunctionTypeT;
typedef enum {superattracting = 100, attracting = 200, parabolic = 300, repelling = 400} DynamicTypeT;
*/
unsigned char Compute8BitColor(FunctionTypeT FunctionType, complex double z){
unsigned char iColor;
switch(DynamicType+FunctionType){
// case FunctionType + DynamicType: {ComputeColor_FunctionType_DynamicType(z); break;}
// FatouBasins
case FatouBasins + superattracting: {iColor = ComputeColor_FatouBasins_superattracting(z); break;}
case FatouBasins + attracting: {iColor = ComputeColor_FatouBasins_attracting(z); break;}
case FatouBasins + parabolic: {iColor = ComputeColor_FatouBasins_parabolic(z); break;}
case FatouBasins + repelling: {iColor = ComputeColor_FatouBasins_repelling(z); break;}
case FatouBasins + dendrite: {iColor = ComputeColor_FatouBasins_dendrite(z); break;}
// FatouComponents
case FatouComponents + superattracting: {iColor = ComputeColor_FatouComponents_superattracting(z); break;}
case FatouComponents + attracting: {iColor = ComputeColor_FatouComponents_attracting(z); break;}
case FatouComponents + parabolic: {iColor = ComputeColor_FatouComponents_parabolic(z); break;}
case FatouComponents + repelling: {iColor = ComputeColor_FatouComponents_repelling(z); break;}
// LSM
case LSM + superattracting: {iColor = ComputeColor_LSM_superattracting(z); break;}
case LSM + attracting: {iColor = ComputeColor_LSM_attracting(z); break;}
case LSM + parabolic: {iColor = ComputeColor_LSM_parabolic(z); break;}
case LSM + repelling: {iColor = ComputeColor_LSM_repelling(z); break;}
case LSM + dendrite: {iColor = ComputeColor_LSM_dendrite(z); break;}
// BDM
case BDM + superattracting: {iColor = ComputeColor_BDM_superattracting(z); break;}
case BDM + attracting: {iColor = ComputeColor_BDM_attracting(z); break;}
case BDM + parabolic: {iColor = ComputeColor_BDM_parabolic(z); break;}
case BDM + repelling: {iColor = ComputeColor_BDM_repelling(z); break;}
case BDM + dendrite: {iColor = ComputeColor_BDM_dendrite(z); break;}
case DEM+ dendrite: {iColor = ComputeColorOfDEMJ(z); break;}
default: break;
}
return iColor;
}
// plots raster point (ix,iy)
int DrawPoint ( unsigned char A[], FunctionTypeT FunctionType, int ix, int iy)
{
int i; /* index of 1D array */
unsigned char iColor;
complex double z;
i = Give_i (ix, iy); /* compute index of 1D array from indices of 2D array */
if(i<0 && i> iMax)
{ return 1;}
z = GiveZ(ix,iy);
iColor = Compute8BitColor(FunctionType, z);
A[i] = iColor ; //
return 0;
}
// this function changes color of all image pixels
int DrawImage ( unsigned char A[], FunctionTypeT FunctionType)
{
unsigned int ix, iy; // pixel coordinate
fprintf (stderr, "compute image %d \t c = %.16f%+.16f*i \n", FunctionType, creal(c), cimag(c));
// for all pixels of image
#pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax, uUnknown, uInterior, uExterior)
for (iy = iyMin; iy <= iyMax; ++iy)
{
fprintf (stderr, " %d from %d \r", iy, iyMax); //info
for (ix = ixMin; ix <= ixMax; ++ix)
DrawPoint(A, FunctionType, ix, iy); //
}
fprintf (stderr, "\n"); //info
return 0;
}
int PlotPoint(const complex double z, unsigned char A[]){
unsigned int ix = (creal(z)-ZxMin)/PixelWidth;
unsigned int iy = (ZyMax - cimag(z))/PixelHeight;
unsigned int i = Give_i(ix,iy); /* index of _data array */
if(i>-1 && i< iMax)
{A[i]= 0; // 255-A[i];
}
return 0;
}
int IsInsideCircle (int x, int y, int xcenter, int ycenter, int r){
double dx = x- xcenter;
double dy = y - ycenter;
double d = sqrt(dx*dx+dy*dy);
if (d<r) { return 1;}
return 0;
}
// Big point = disk
int PlotBigPoint(const complex double z, double p_size, unsigned char A[]){
unsigned int ix_seed = (creal(z)-ZxMin)/PixelWidth;
unsigned int iy_seed = (ZyMax - cimag(z))/PixelHeight;
unsigned int i;
//unsigned char temp;
if ( is_z_outside(z))
{fprintf (stdout,"PlotBigPoint : z= %.16f %+.16f*I is outside\n", creal(z), cimag(z)); return 1;} // do not plot
/* mark seed point by big pixel */
int iSide =p_size*iWidth/2000.0 ; /* half of width or height of big pixel */
int iY;
int iX;
for(iY=iy_seed-iSide;iY<=iy_seed+iSide;++iY){
for(iX=ix_seed-iSide;iX<=ix_seed+iSide;++iX){
if (IsInsideCircle(iX, iY, ix_seed, iy_seed, iSide)) {
i= Give_i(iX,iY); /* index of _data array */
//if(i>-1 && i< iMax)
//temp = A[i];
//if ( temp > 110 && temp < 160)
// { A[i] = 0; }
// else {A[i]= 255 - temp ; }
A[i] = 0;
}
// else {printf(" bad point \n");}
}}
return 0;
}
int DrawForwardOrbit(const complex double z0, const unsigned long long int i_Max, double p_size, unsigned char A[]){
unsigned long long int i; /* nr of point of critical orbit */
complex double z = z0;
//complex double zt = f(f(z));
fprintf(stdout, "draw forward orbit \n");
fprintf(stderr, "draw forward orbit \n");
PlotBigPoint(z, p_size, A);
/* forward orbit of critical point */
for (i=1;i<i_Max ; ++i)
{
z = f(z);
//if (cabs2(z - zp) < AR2) {break;} //
if (cabs2(z - zp) < PixelWidth2)
{ fprintf (stdout,"last point of the orbit z= %.16f %+.16f*I \n After i = %llu iterations forward orbit of critical point reaches trap: circle with radius = PixelWidth around fixed point \n", creal(z), cimag(z), i );
break;} //
//if (cabs2(z-zt) > PixelWidth2)
PlotBigPoint(z, p_size/2 , A);
//zt = z;
}
zcr_last = z;
fprintf (stdout,"first point of the orbit z0= %.16f %+.16f*I \n", creal(z0), cimag(z0));
// printf (stdout,"last point of the orbit z= %.16f %+.16f*I \n After i = %llu iterations forward orbit of critical point reaches trap: circle with radius = AR around fixed point \n", creal(z), cimag(z), i );
fprintf (stdout,"last point of the orbit z= %.16f %+.16f*I after i = %llu iterations. \n", creal(z), cimag(z), i);
fprintf (stdout,"distance between last point of the orbit and fixed point = %.16f = %.16f * ImageWidth = %.1f * PixelWidth = \n ", cabs(z - zp), cabs(z-zp)/(ZxMax - ZxMin), cabs(z - zp)/PixelWidth);
fprintf (stdout,"\n \n ");
return 0;
}
// ***********************************************************************************************
// ********************** draw line segment ***************************************
// ***************************************************************************************************
// plots raster point (ix,iy)
int iDrawPoint(unsigned int ix, unsigned int iy, unsigned char iColor, unsigned char A[])
{
/* i = Give_i(ix,iy) compute index of 1D array from indices of 2D array */
if (ix >=ixMin && ix<=ixMax && iy >=iyMin && iy<=iyMax )
{A[Give_i(ix,iy)] = iColor;}
else {fprintf (stderr,"iDrawPoint : (%d; %d) is outside\n", ix,iy); }
return 0;
}
/*
http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm
Instead of swaps in the initialisation use error calculation for both directions x and y simultaneously:
*/
void iDrawLine( int x0, int y0, int x1, int y1, unsigned char iColor, unsigned char A[])
{
int x=x0; int y=y0;
int dx = abs(x1-x0), sx = x0<x1 ? 1 : -1;
int dy = abs(y1-y0), sy = y0<y1 ? 1 : -1;
int err = (dx>dy ? dx : -dy)/2, e2;
for(;;){
iDrawPoint(x, y, iColor, A);
if (x==x1 && y==y1) break;
e2 = err;
if (e2 >-dx) { err -= dy; x += sx; }
if (e2 < dy) { err += dx; y += sy; }
}
}
int dDrawLineSegment(double complex Z0, double complex Z1, int color, unsigned char *array)
{
double Zx0 = creal(Z0);
double Zy0 = cimag(Z0);
double Zx1 = creal(Z1);
double Zy1 = cimag(Z1);
unsigned int ix0, iy0; // screen coordinate = indices of virtual 2D array
unsigned int ix1, iy1; // screen coordinate = indices of virtual 2D array
// first step of clipping
//if ( Zx0 < ZxMax && Zx0 > ZxMin && Zy0 > ZyMin && Zy0 <ZyMax
// && Zx1 < ZxMax && Zx1 > ZxMin && Zy1 > ZyMin && Zy1 <ZyMax )
ix0= (Zx0- ZxMin)/PixelWidth;
iy0 = (ZyMax - Zy0)/PixelHeight; // inverse Y axis
ix1= (Zx1- ZxMin)/PixelWidth;
iy1= (ZyMax - Zy1)/PixelHeight; // inverse Y axis
// second step of clipping
if (ix0 >=ixMin && ix0<=ixMax && ix0 >=ixMin && ix0<=ixMax && iy0 >=iyMin && iy0<=iyMax && iy1 >=iyMin && iy1<=iyMax )
iDrawLine(ix0,iy0,ix1,iy1,color, array) ;
return 0;
}
// ***********************************************************************************************
// ********************** mark traps ***************************************
// ***************************************************************************************************
int Mark_Parabolic_Components_Triangle_Trap(unsigned char A[]){
unsigned int ix, iy; // pixel coordinate
unsigned int i;
unsigned char temp;
fprintf (stderr, "Mark_Parabolic_Components_Triangle_Trap\n");
// for all pixels of image
#pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax)
for (iy = iyMin; iy <= iyMax; ++iy)
{
fprintf (stderr, " %d from %d \r", iy, iyMax); //info
for (ix = ixMin; ix <= ixMax; ++ix){
if ( IsPointIn_Parabolic_Components_Triangle(GiveZ(ix,iy))){
i= Give_i(ix,iy); /* index of _data array */
//A[i]= 255-A[i]; // inverse color
temp = A[i];
if ( temp > 110 && temp < 160)
{ A[i] = 0; }
else {A[i]= 255 - temp ; }
}}}
return 0;
}
int Mark_parabolic_BDM_Triangle_Traps(unsigned char A[]){
unsigned int ix, iy; // pixel coordinate
unsigned int i;
complex double z;
fprintf (stderr, "Mark_Parabolic_Components_Triangle_Trap\n");
// for all pixels of image
#pragma omp parallel for schedule(dynamic) private(ix,iy,i,z) shared(A, ixMax , iyMax)
for (iy = iyMin; iy <= iyMax; ++iy)
{
fprintf (stderr, " %d from %d \r", iy, iyMax); //info
for (ix = ixMin; ix <= ixMax; ++ix){
z = GiveZ(ix,iy);
i= Give_i(ix,iy); /* index of _data array */
// mark traps
if (IsPointIn_BDM_TriangleB(z)){ A[i] = 200;}
if (IsPointIn_BDM_TriangleA(z)){ A[i] = 100;}
}}
return 0;
}
// ***********************************************************************************************
// ********************** mark immediate basin of attracting cycle***************************************
// ***************************************************************************************************
int FillContour(complex double seed, unsigned char color, unsigned char _data[])
{
/*
fills contour with black border ( color = iColorOfBoundary) using seed point inside contour
and horizontal lines
it starts from seed point, saves max right( iXmaxLocal) and max left ( iXminLocal) interior points of horizontal line,
in new line ( iY+1 or iY-1) it computes new interior point : iXmidLocal=iXminLocal + (iXmaxLocal-iXminLocal)/2;
result is stored in _data array : 1D array of 1-bit colors ( shades of gray)
it does not check if index of _data array is good so memory error is possible
it need array with components boundaries mrked by iColorOfBoundary
*/
double dXseed = creal(seed);
double dYseed = cimag(seed);
// from
int iXseed = (int)((dXseed - ZxMin)/PixelWidth);
int iYseed = (int)((ZyMax - dYseed )/PixelHeight); // reversed Y axis
int iX; /* seed integer coordinate */
int iY = iYseed;
/* most interior point of line iY */
int iXmidLocal=iXseed;
/* min and max of interior points of horizontal line iY */
int iXminLocal;
int iXmaxLocal;
int i ; /* index of _data array */;
//fprintf (stderr, "FillContour seed = %.16f %+.16f = %d %+d\n",creal(seed), cimag(seed), iXseed,iYseed);
/* --------- move up --------------- */
do{
iX=iXmidLocal;
i =Give_i(iX,iY); /* index of _data array */;
/* move to right */
while (_data[i] != iColorOfBoundary)
{ _data[i]=color;
iX+=1;
i=Give_i(iX,iY);
}
iXmaxLocal=iX-1;
/* move to left */
iX=iXmidLocal-1;
i=Give_i(iX,iY);
while (_data[i] != iColorOfBoundary)
{ _data[i]=color;
iX-=1;
i=Give_i(iX,iY);
}
iXminLocal=iX+1;
iY+=1; /* move up */
iXmidLocal=iXminLocal + (iXmaxLocal-iXminLocal)/2; /* new iX inside contour */
i=Give_i(iXmidLocal,iY); /* index of _data array */;
if ( _data[i] == iColorOfBoundary) break; /* it should not cross the border */
} while (iY<iyMax);
/* ------ move down ----------------- */
iXmidLocal=iXseed;
iY=iYseed-1;
do{
iX=iXmidLocal;
i =Give_i(iX,iY); /* index of _data array */;
/* move to right */
while (_data[i] != iColorOfBoundary) /* */
{ _data[i]=color;
iX+=1;
i=Give_i(iX,iY);
}
iXmaxLocal=iX-1;
/* move to left */
iX=iXmidLocal-1;
i=Give_i(iX,iY);
while (_data[i] != iColorOfBoundary) /* */
{ _data[i]=color;
iX-=1; /* move to right */
i=Give_i(iX,iY);
}
iXminLocal=iX+1;
iY-=1; /* move down */
iXmidLocal=iXminLocal + (iXmaxLocal-iXminLocal)/2; /* new iX inside contour */
i=Give_i(iXmidLocal,iY); /* index of _data array */;
if ( _data[i]== iColorOfBoundary) break; /* it should not cross the border */
} while (0<iY);
//fprintf (stderr, "FillContour done \n");
return 0;
}
// fill countours of componnets of immediate basin of attraction
// with color
// needs zpp and period global var
// it needs componnets boundaris in A array !!!!
int MarkImmediateBasin( unsigned char A[]){
fprintf (stderr, "mark immediate basin of attracting cycle \n");
//printf(" \n");
unsigned char iColor = 100;
//for (int i=0;i<period ; ++i){
FillContour(zp, iColor , A);
//}
return 0;
}
// ***********************************************************************************************
// ********************** edge detection usung Sobel filter ***************************************
// ***************************************************************************************************
// from Source to Destination
int ComputeBoundaries(unsigned char S[], unsigned char D[])
{
unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
unsigned int i; /* index of 1D array */
/* sobel filter */
unsigned char G, Gh, Gv;
// boundaries are in D array ( global var )
// clear D array
memset(D, iColorOfBasin1, iSize*sizeof(*D)); // for heap-allocated arrays, where N is the number of elements = FillArrayWithColor(D , iColorOfBasin1);
// printf(" find boundaries in S array using Sobel filter\n");
#pragma omp parallel for schedule(dynamic) private(i,iY,iX,Gv,Gh,G) shared(iyMax,ixMax)
for(iY=1;iY<iyMax-1;++iY){
for(iX=1;iX<ixMax-1;++iX){
Gv= S[Give_i(iX-1,iY+1)] + 2*S[Give_i(iX,iY+1)] + S[Give_i(iX-1,iY+1)] - S[Give_i(iX-1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX+1,iY-1)];
Gh= S[Give_i(iX+1,iY+1)] + 2*S[Give_i(iX+1,iY)] + S[Give_i(iX-1,iY-1)] - S[Give_i(iX+1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX-1,iY-1)];
G = sqrt(Gh*Gh + Gv*Gv);
i= Give_i(iX,iY); /* compute index of 1D array from indices of 2D array */
if (G==0) {D[i]=255;} /* background */
else {D[i]=0;} /* boundary */
}
}
return 0;
}
// copy from source array S to destination array D
int CopyBoundaries(unsigned char S[], unsigned char D[])
{
unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
unsigned int i; /* index of 1D array */
//printf("copy boundaries from S array to D array \n");
for(iY=1;iY<iyMax-1;++iY)
for(iX=1;iX<ixMax-1;++iX)
{i= Give_i(iX,iY); if (S[i]==0) D[i]=0;}
return 0;
}
// *******************************************************************************************
// ********************************** Boundary = DEM/J ****************************
// *********************************************************************************************
int DrawJuliaSetBoundary_using_DEMJ ( unsigned char A[])
{
unsigned int ix, iy; // pixel coordinate
fprintf (stderr, "compute image DEM/J c = %.16f%+.16f*i \n", creal(c), cimag(c));
// for all pixels of image
#pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax, uUnknown, uInterior, uExterior)
for (iy = iyMin; iy <= iyMax; ++iy)
{
fprintf (stderr, " %d from %d \r", iy, iyMax); //info
for (ix = ixMin; ix <= ixMax; ++ix)
// DrawPoint(A, FunctionType, ix, iy); //
{
int i; /* index of 1D array */
unsigned char iColor;
complex double z;
i = Give_i (ix, iy); /* compute index of 1D array from indices of 2D array */
//if(i<0 && i> iMax)
// { return 1;}
z = GiveZ(ix,iy);
double distance = compute_distance(z); // positive number if escaping, negative if not escaping
if (distance < distanceMax && distance > 0.0){
double g = tanh(distance);
iColor = 255*g;
A[i] = iColor; }
}
}
fprintf (stderr, "\n"); //info
return 0;
}
// *******************************************************************************************
// ********************************** save grey A array to pgm file ****************************
// *********************************************************************************************
int SaveArray2PGMFile (unsigned char A[], complex double c, char * n, unsigned int iHeight, char *comment)
{
FILE *fp;
const unsigned int MaxColorComponentValue = 255; /* color component is coded from 0 to 255 ; it is 8 bit color file */
char name[100]; /* name of file */
snprintf (name, sizeof name, "%s_%.16f%+.16f*I_%d_%.3f",n, creal(c),cimag(c), iHeight, t2); /* radius and iHeght are global variables */
char *filename = strcat (name, ".pgm");
char long_comment[200]; // to long comment can cause: "*** stack smashing detected ***: terminated"
sprintf (long_comment, "%s %s", f_description , comment); // f_description is global var
// save image array to the pgm file
fp = fopen (filename, "wb"); // create new file,give it a name and open it in binary mode
fprintf (fp, "P5\n # %s\n %u %u\n %u\n", long_comment, iWidth, iHeight, MaxColorComponentValue); // write header to the file
size_t rSize = fwrite (A, sizeof(A[0]), iSize, fp); // write whole array with image data bytes to the file in one step
fclose (fp);
// info
if ( rSize == iSize)
{
printf ("File %s saved ", filename);
if (long_comment == NULL || strlen (long_comment) == 0)
printf ("\n");
else { printf (". Comment = %s \n", long_comment); }
}
else {printf("wrote %zu elements out of %llu requested\n", rSize, iSize);}
NumberOfImages +=1; // count images using global variable
return 0;
}
// *******************************************************************************************
// ********************************** save A array to ppm file ****************************
// *********************************************************************************************
int Save_PPM( const unsigned char A[], const char* sName, const char* comment, const double radius )
{
FILE * fp;
char name [100]; /* name of file */
snprintf(name, sizeof name, "%s_%f", sName, radius); /* */
char *filename =strcat(name,".ppm");
char long_comment[200];
sprintf (long_comment, "fc(z)=z^2+ c %s", comment);
// save image to the pgm file
fp= fopen(filename,"wb"); // create new file,give it a name and open it in binary mode
if (!fp ) { fprintf( stderr, "ERROR saving ( cant open) file %s \n", filename); return 1; }
// else
fprintf(fp,"P6\n%d %d\n255\n", iWidth, iHeight); // write header to the file
size_t rSize = fwrite(A, sizeof(A[0]), iSize_rgb, fp); // write array with image data bytes to the file in one step
fclose(fp);
// info
if ( rSize == iSize_rgb)
{
printf ("File %s saved ", filename);
if (long_comment == NULL || strlen (long_comment) == 0)
{printf ("\n"); }
else { printf (". Comment = %s \n", long_comment); }
}
else {printf("wrote %zu elements out of %u requested\n", rSize, iSize_rgb);}
//
NumberOfImages +=1; // count images using global variable
return 0;
}
int PrintCInfo ()
{
printf ("gcc version: %d.%d.%d\n", __GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__); // https://stackoverflow.com/questions/20389193/how-do-i-check-my-gcc-c-compiler-version-for-my-eclipse
// OpenMP version is displayed in the console : export OMP_DISPLAY_ENV="TRUE"
printf ("__STDC__ = %d\n", __STDC__);
printf ("__STDC_VERSION__ = %ld\n", __STDC_VERSION__);
printf ("c dialect = ");
switch (__STDC_VERSION__)
{ // the format YYYYMM
case 199409L:
printf ("C94\n");
break;
case 199901L:
printf ("C99\n");
break;
case 201112L:
printf ("C11\n");
break;
case 201710L:
printf ("C18\n");
break;
//default : /* Optional */
}
return 0;
}
int
PrintProgramInfo ()
{
// display info messages
fprintf (stdout, "Program version = %d \n", PROGRAM_VERSION ); // https://stackoverflow.com/questions/12509038/can-i-print-defines-given-their-values-in-c
fprintf (stdout, "%s \n", f_description );
fprintf (stdout, "c = %.16f %+.16f*i \n", creal (c), cimag (c));
double ImageWidth = (ZxMax - ZxMin);
fprintf (stdout, "DynamicType value is setup manually; One can do it also numerically ( from multiplier of fixed point alfa or from some other properities)\n");
switch ( DynamicType){
case repelling:
fprintf (stdout, "\tThere is only one Fatou basin: basin of infinity \n");
fprintf (stdout, "\tthere is no interior = Julia set is disconnected \n");
fprintf (stdout, "\tcritical point z=0 is repelling = attracted to infinity \n");
break;
case attracting:
fprintf (stdout, "\tbasin type is attracting \n");
fprintf (stdout, "\tzcr_last = %.16f \talfa fixed point zp = %.16f\n", creal (zcr_last), creal(zp));//
fprintf (stdout, "\tdelta = %.16f is the distance between fixed points\n", delta);//
fprintf (stdout, "\tAtracting Radius AR is set manually = %.16f = %f * PixelWidth = %f * ImageWidth \n", AR, AR / PixelWidth, AR /ImageWidth );
break;
case superattracting:
fprintf (stdout, "\tbasin type is superattracting \n");
fprintf (stdout, "\there superattracting periodic point ie equall to critical point : zcr = %.16f = zp = %.16f\n", creal (zcr), creal(zp));//
fprintf (stdout, "\tAtracting Radius AR is set manually = %.16f = %f *PixelWidth = %f *ImageWidth \n", AR, AR / PixelWidth, AR /ImageWidth);
break;
case parabolic:
fprintf (stdout, "\tbasin type is parabolic \n");
fprintf (stdout, "\t parabolic trap for Julia set components is a triangle: ( z1,z2,z3) = part of the circle around parabolic fixed point\n");
fprintf (stdout, "\t z2 and z3 are computed in other program \n");
fprintf (stdout, "\tz1 = %.16f %+.16f*I\n", creal (z1), cimag(z1));//
fprintf (stdout, "\tz2 is a parabolic fixed point zp = %.16f %+.16f*I\n", creal (zp), cimag(zp));//
fprintf (stdout, "\tz3 = %.16f %+.16f*I\n", creal (z3), cimag(z3));//
fprintf (stdout, "\t for parabolic trap for Julia set components see procedure: IsPointIn_Parabolic_Components_Triangle\n");
break;
case dendrite:
case siegel:
default: break;
}
fprintf (stdout, "Image Width = %f in world coordinate\n", ImageWidth);
fprintf (stdout, "PixelWidth = %.16f \n", PixelWidth);
fprintf (stdout, "plane description \n");
fprintf (stdout, "\tcenter z = %.16f %+.16f*i and radius = %.16f \n", creal (center), cimag (center), radius);
// center and radius
// center and zoom
// GradientRepetition
fprintf (stdout, "Maximal number of iterations = iterMax = %d \n", IterMax);
fprintf (stdout, "Maximal number of iterations = iterMax_LSM = %d \n", IterMax_LSM);
fprintf (stdout, "ratio of image = %f ; it should be 1.000 ...\n", ratio);
fprintf (stdout, "t0 = %.16f = %d / %d\n", t0, t_numerator, t_denominator);
fprintf (stdout, "\tEscaping Radius = ER = %.16f = %f *PixelWidth = %f * ImageWidth \n", ER, ER / PixelWidth, ER /ImageWidth);
fprintf(stdout, " periodic point ");
//for (int i=0;i<period ; ++i){
fprintf(stdout, "z = %.16f %+.16f*i \n", creal (zp), cimag (zp));
//}
fprintf (stdout, "Unknown pixels = %llu = %.16f * iSize \n", uUnknown, ((double) uUnknown)/iSize );
fprintf (stdout, "Exterior pixels = %llu = %.16f * iSize \n", uExterior, ((double) uExterior)/iSize );
fprintf (stdout, "Interior pixels = %llu = %.16f * iSize \n", uInterior, ((double) uInterior)/iSize );
//printf("Number of images = %d \n", NumberOfImages);
return 0;
}
int SetPlane(complex double center, double radius, double a_ratio){
ZxMin = creal(center) - radius*a_ratio;
ZxMax = creal(center) + radius*a_ratio; //0.75;
ZyMin = cimag(center) - radius; // inv
ZyMax = cimag(center) + radius; //0.7;
return 0;
}
// Check Orientation of z-plane image : mark first quadrant of complex plane
// it should be in the upper right position
// uses global var : ...
int CheckZPlaneOrientation(unsigned char A[] )
{
double Zx, Zy; // Z= Zx+ZY*i;
unsigned i; /* index of 1D array */
unsigned int ix, iy; // pixel coordinate
fprintf(stderr, "compute image CheckOrientation\n");
// for all pixels of image
#pragma omp parallel for schedule(dynamic) private(ix,iy, i, Zx, Zy) shared(A, ixMax , iyMax)
for (iy = iyMin; iy <= iyMax; ++iy){
//fprintf (stderr, " %d from %d \r", iy, iyMax); //info
for (ix = ixMin; ix <= ixMax; ++ix){
// from screen to world coordinate
Zy = GiveZy(iy);
Zx = GiveZx(ix);
i = Give_i(ix, iy); /* compute index of 1D array from indices of 2D array */
if (Zx>0 && Zy>0) A[i]=255-A[i]; // check the orientation of Z-plane by marking first quadrant */
}
}
return 0;
}
// *****************************************************************************
//;;;;;;;;;;;;;;;;;;;;;; setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
// **************************************************************************************
int local_setup(){
switch ( DynamicType){
case repelling: // no interior = no attracting fixed point = only escaping points
break;
case attracting:
delta = csqrt(1.0 - 4.0*c); // delta is a distance between alfa and beta fixed points
AR = (delta /3.5) * iWidth / 2000;
break;
case superattracting: // cabs(zp - zcr_last ) < PixelWidth
AR = 30.0* PixelWidth * iWidth / 2000 ; //
break;
case parabolic:
/* Target set for the components for child period:
* 1 and 2: target set can be circle with parabolic fixed point on it's boundary ( target set is inside component )
* > 2: target set is a triangle fragment of circle with center at parabolic fixed point
parabolic trap is a triangle: ( z1,z2,z3) = part of the circle around parabolic fixed point
z2 and z3 are computed in other program
*/
Describe_Triangle(z1, zp, z3); // test if triangle is oriented counterclockwise
AR = cabs(zp-z1);
R_BDM = cabs(-0.0559603266109820 -0.1163177312664140*I); // it is a point from BDM trap // 20.0* PixelWidth * iWidth / 2000 ; //
break;
default: break;
}
AR2 = AR*AR;
R2_BDM = R_BDM* R_BDM;
return 0;
}
int general_setup()
{
fprintf (stderr, "setup start\n");
zp = GiveFixed(c);
center = 0.0; //zp;
radius = 1.5; //0.24;
z13 = (z1+z3)/2.0;
/* 2D array ranges */
iWidth = iHeight* DisplayAspectRatio ;
iSize = iWidth * iHeight; // size = number of points in array
iSize_rgb = iSize* iColorSize;
// iy
iyMax = iHeight - 1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
//ix
ixMax = iWidth - 1;
/* 1D array ranges */
// i1Dsize = i2Dsize; // 1D array with the same size as 2D array
iMax = iSize - 1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
SetPlane( center, radius, DisplayAspectRatio );
/* Pixel sizes */
PixelWidth = (ZxMax - ZxMin) / ixMax; // ixMax = (iWidth-1) step between pixels in world coordinate
PixelHeight = (ZyMax - ZyMin) / iyMax;
ratio = ((ZxMax - ZxMin) / (ZyMax - ZyMin)) / ((double) iWidth / (double) iHeight); // it should be 1.000 ...
PixelWidth2 = PixelWidth*PixelWidth;
// LSM
// escape radius ( of circle around infinity
ER = 2000.0; // it can be 2.0: but then there is no level curves near Julia set; but the small detailes will be visible // exp(M_PI);
ER2 = ER*ER;
t0 = ((double) t_numerator)/t_denominator; //1.0 / period; // Is it iternal angle from internal adress ???
// DEM
BoundaryWidth = 2.0*iWidth/2000.0;
distanceMax = BoundaryWidth*PixelWidth; // here boundary is changing with resolution, maybe % of ImageWidth would be better ?
/* create dynamic 1D arrays for colors ( shades of gray ) */
data = malloc (iSize * sizeof (unsigned char));
edge = malloc (iSize * sizeof (unsigned char));
edge2 = malloc (iSize * sizeof (unsigned char));
rgbData = malloc (iSize_rgb * sizeof (unsigned char));
if (data == NULL || edge == NULL || edge2 == NULL || rgbData == NULL)
{ fprintf (stderr, " Could not allocate memory"); return 1; }
fprintf (stderr, " end of setup \n");
return 0;
} // ;;;;;;;;;;;;;;;;;;;;;;;;; end of the setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
int end(void)
{
fprintf(stderr, " allways free memory (deallocate ) to avoid memory leaks \n"); // https://en.wikipedia.org/wiki/C_dynamic_memory_allocation
fprintf(stderr, " warning: too long comment in SaveArray2PGMFile can cause: *** stack smashing detected ***: terminated\n");
free (data);
free(edge);
free(edge2);
free(rgbData);
PrintCInfo ();
return 0;
}
int MakeImages( ){
// warning: to long comment in SaveArray2PGMFile can cause: "*** stack smashing detected ***: terminated"
/*
DrawImage (data, FatouBasins);
SaveArray2PGMFile (data, c, "FatouBasins" , "FatouBasins ");
ComputeBoundaries(data,edge);
SaveArray2PGMFile (edge, c, "FatouBasins_LCM" , "FatouBasins_LCM ");
CopyBoundaries(edge, data);
SaveArray2PGMFile (data, c, "FatouBasins_LSCM" , "FatouBasins_LSCM");
DrawForwardOrbit(zcr, 11*IterMax_LSM, 2, data);
SaveArray2PGMFile (data, c, "FatouBasins_CRO" , "boundaries of Level set method ( LSM) = Level Curve Method (LCM) and critical orbit ");
//Mark_Parabolic_Components_Triangle_Trap(data);
//SaveArray2PGMFile (data, c, "FatouBasins_trap" , "FatouBasins trap");
*/
/*
DrawImage (data, FatouComponents);
SaveArray2PGMFile (data, c, "FatouComponents" , "FatouComponents ");
ComputeBoundaries(data,edge);
SaveArray2PGMFile (edge, c, "FatouComponents_LCM" , "FatouComponents_LCM ");
CopyBoundaries(edge, data);
SaveArray2PGMFile (data, c, "FatouComponents_LSCM" , "FatouComponents_LSCM");
DrawForwardOrbit(zcr, 11*IterMax_LSM, 4, data);
SaveArray2PGMFile (data, c, "FatouComponents_LSCM_CRO" , "FatouComponents_LSCM and critical orbit ");
Mark_Parabolic_Components_Triangle_Trap(data);
SaveArray2PGMFile (data, c, "FatouComponents_LSCM_CRO_trap" , "FatouComponents_LSCM, trap and critical orbit ");
*/
/*
Mark_Parabolic_Components_Triangle_Traps(data);
SaveArray2PGMFile (data, "FatouComponents_LSCM_trap" , "FatouComponents_LSCM_trap");
// DrawAttractors(zp3, period, 10, data);
//SaveArray2PGMFile (data, "FatouComponents_LSCM_zp" , "FatouComponents_LSCM_zp");_
DrawImage (data, FatouBasins);
ComputeBoundaries(data,edge);
MarkImmediateBasin(edge); //
SaveArray2PGMFile (edge, "FatouBasins_LCM_immediate" , "FatouBasins_LCM_immediate");
//DrawAttractors(zp3, period, 10, edge);
//SaveArray2PGMFile (edge, "FatouBasins_LCM_immediate_zp" , "FatouBasins_LCM_immediate_zp");
*/
DrawImage (data, LSM);
SaveArray2PGMFile (data, c, "LSM" , iHeight, " LSM/J = Level sets of integer escape time of ET ");
ComputeBoundaries(data,edge);
SaveArray2PGMFile (edge, c, "LCM" , iHeight, "boundaries of LSM/J ( integer Escape Time )= Level Curve ( LC) of integer Escape Time");
CopyBoundaries(edge, data);
SaveArray2PGMFile (data, c, "LSCM" , iHeight, " Level sets and it's baundaries ( Level Curves = LC) of integer escape time of ET ");
/*
DrawImage (data, BDM);
SaveArray2PGMFile (data, c, "BDM" , iHeight, "BDM = Binary Decomposition Method for both exterior and interior = Level Sets of BDM");
ComputeBoundaries(data,edge);
SaveArray2PGMFile (edge, c, "BDM_LC", iHeight, "boundaries of Binary Decomposition Method (LC of BD) = LCBD");
CopyBoundaries( edge, data);
SaveArray2PGMFile (data, c, "BDM_LC_LS" , iHeight, " Binary Decomposition Method for both exterior and interior ");
*/
//CopyBoundaries(edge2, data); // if LSM was done !!!!
//SaveArray2PGMFile (data, c, "BDM_LSLCET" , " Level sets and it's baundaries ( Level Curves = LC) of integer escape time of ET ");
// Mark_parabolic_BDM_Triangle_Traps(data);
//SaveArray2PGMFile (data, c, "BDM_LC_LS_traps", iHeight, "BDM and traps");
//CopyBoundaries(edge2, edge);
//SaveArray2PGMFile (edge, c, "LCBDET ", "boundaries of Binary Decomposition Method and Level sets of Integer Escape Time");
//Mark_Parabolic_Components_Triangle_Trap(edge2);
//SaveArray2PGMFile (edge2, c, "LSM_CRO_trap" , "LSM, critical orbit and trap");
//CopyBoundaries(edge2, data);
//SaveArray2PGMFile (data, "LSCM" , "LSCM");
DrawImage (data, DEM);
SaveArray2PGMFile (data, c, "DEM" , iHeight, "DEM/J = Distance Estimation Method for both exterior and interior of Julia set");
DrawImage (data, BDM);
SaveArray2PGMFile (data, c, "BDM" , iHeight, "BDM = Binary Decomposition Method for both exterior of Julia set. Dendrite Julia set = there is no interior");
ComputeBoundaries(data,edge2);
SaveArray2PGMFile (edge2, c, "BDM_boundaries" , iHeight, "boundaries of BDM ");
DrawJuliaSetBoundary_using_DEMJ ( data );
SaveArray2PGMFile (data, c, "DEM_BDM" , iHeight, "BDM and DEM/J = Distance Estimation Method for exterior of Julia set. Dendrite Julia set = there is no interior");
CopyBoundaries(edge, data);
SaveArray2PGMFile (data, c, "DEM_BDM_LCM" , iHeight, "LCM, BDM and DEM/J = Distance Estimation Method for exterior of Julia set. Dendrite Julia set = there is no interior");
CopyBoundaries(edge, edge2);
SaveArray2PGMFile (edge2, c, "BDM_LSM_boundaries" , iHeight, "boundaries of BDM and LSM/J");
return 0;
}
// ********************************************************************************************************************
/* ----------------------------------------- main -------------------------------------------------------------*/
// ********************************************************************************************************************
int main(void)
{
DynamicType = dendrite; // setup DynamicType value manually ; One can do it also numerically ( from multiplier or from some properities)
general_setup();
local_setup();
MakeImages();
PrintProgramInfo();
end();
return 0;
}
bash source code
[edit]_%3D_z%5E2_%2B_i_using_BDM_DEM_LSM.png&action=edit§ion=3){kind=link}
#!/bin/bash
# script file for BASH
# which bash
# save this file as n.sh
# chmod +x n.sh
# ./n.sh
# checked in https://www.shellcheck.net/
printf "make pgm files \n"
gcc n.c -lm -Wall -march=native -fopenmp
if [ $? -ne 0 ]
then
echo ERROR: compilation failed !!!!!!
exit 1
fi
export OMP_DISPLAY_ENV="TRUE"
printf "display OMP info \n"
printf "run the compiled program\n"
time ./a.out > n.txt
export OMP_DISPLAY_ENV="FALSE"
printf "change Image Magic settings\n"
export MAGICK_WIDTH_LIMIT=100MP
export MAGICK_HEIGHT_LIMIT=100MP
printf "convert all pgm files to png using Image Magic v 6 convert \n"
# for all pgm files in this directory
for file in *.pgm ; do
# b is name of file without extension
b=$(basename "$file" .pgm)
# convert using ImageMagic
convert "${b}".pgm -resize 2000x2000 "${b}".png
#convert "${b}".pgm "${b}".png
echo "$file"
done
printf "delete all pgm files \n"
rm ./*.pgm
echo OK
printf "info about software \n"
bash --version
make -v
gcc --version
convert -version
convert -list resource
# end
make
[edit]_%3D_z%5E2_%2B_i_using_BDM_DEM_LSM.png&action=edit§ion=4){kind=link}
all:
chmod +x d.sh
./d.sh
Tu run the program simply
make
text output
[edit]_%3D_z%5E2_%2B_i_using_BDM_DEM_LSM.png&action=edit§ion=5){kind=link}
Licensing
[edit]_%3D_z%5E2_%2B_i_using_BDM_DEM_LSM.png&action=edit§ion=6){kind=link}
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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|---|---|---|---|---|---|
| current | 18:50, 2 September 2023 | | 2,000 × 2,000 (658 KB) | Soul windsurfer (talk | contribs) | Uploaded own work with UploadWizard |
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