Category:Number pyramid Liana (image set)
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This category is an image set. It should contain only images that have the same style, and should have a parent category that is purely topical.
See also category: Number pyramid Ivy (image set).v:Seal (discrete mathematics), v:Template:Seal pyramids Liana and Ivy
top to bottom: arity back to front: depth left to right: valency
All indices go from 1 to 7. The entries Liana(0, arity, 0) = 1 are not shown.
The entries of Liana are the column sums of Ivy.
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#version 3.6;
global_settings { assumed_gamma 1.0 }
#default{ finish{ ambient 0.1 diffuse 0.9 conserve_energy}}
#include "colors.inc"
#declare Camera_Position = vnormalize(<13.2, 7.8, -45>) * 35;
camera{
orthographic
location Camera_Position
right x*image_width/image_height
angle 12.5
look_at <.05, 0, 0>
}
light_source{ <-400, 500, -300> color White*0.9 shadowless}
light_source{ <400, 200, 100> color White*0.7 shadowless}
light_source{ Camera_Position color rgb<0.9,0.9,1>*0.3 shadowless}
sky_sphere{ pigment{ White } }
////////////////////////////////////////////////////////////////////////////////////// squares
#declare EdgeRadius = .006;
#macro put_square(n)
union{
#for(i, 0, n)
cylinder{<1, 7-n, 7-i>, <n+1, 7-n, 7-i>, EdgeRadius}
#end
#for(i, 0, n)
cylinder{<i+1, 7-n, 7>, <i+1, 7-n, 7-n>, EdgeRadius}
#end
pigment{color srgbt <.6, .6, .6, .5>}
}
#end
#declare Squares = union{
#for(n, 1, 6)
put_square(n)
#end
}
////////////////////////////////////////////////////////////////////////////////////// numbers
#declare TextScale = .22;
#declare TextDepth = .075;
#declare FontPath = "/usr/share/fonts/truetype/msttcorefonts/Arial.ttf";
#macro put_number(depth, arity, valency, entry)
#if(arity = 7) // highlight
#declare Color = srgb <.95, 0, 0>;
#else
#declare Color = srgb .25;
#end
#declare px = valency;
#declare py = 8 - arity;
#declare pz = 8 - depth;
#local TextObject = text{ttf FontPath, str(entry, 0, 0), TextDepth, 0 scale TextScale}
object{
TextObject
translate -x * ( max_extent(TextObject).x - min_extent(TextObject).x ) / 2
pigment{color Color}
translate <px - .01, py - .07, pz - .02>
}
#end
#declare Numbers = union{
put_number(1, 1, 1, 1)
put_number(1, 2, 1, 2)
put_number(1, 2, 2, 1)
put_number(1, 3, 1, 3)
put_number(1, 3, 2, 3)
put_number(1, 3, 3, 1)
put_number(1, 4, 1, 4)
put_number(1, 4, 2, 6)
put_number(1, 4, 3, 4)
put_number(1, 4, 4, 1)
put_number(1, 5, 1, 5)
put_number(1, 5, 2, 10)
put_number(1, 5, 3, 10)
put_number(1, 5, 4, 5)
put_number(1, 5, 5, 1)
put_number(1, 6, 1, 6)
put_number(1, 6, 2, 15)
put_number(1, 6, 3, 20)
put_number(1, 6, 4, 15)
put_number(1, 6, 5, 6)
put_number(1, 6, 6, 1)
put_number(1, 7, 1, 7)
put_number(1, 7, 2, 21)
put_number(1, 7, 3, 35)
put_number(1, 7, 4, 35)
put_number(1, 7, 5, 21)
put_number(1, 7, 6, 7)
put_number(1, 7, 7, 1)
put_number(2, 2, 2, 1)
put_number(2, 3, 2, 3)
put_number(2, 3, 3, 4)
put_number(2, 4, 2, 6)
put_number(2, 4, 3, 16)
put_number(2, 4, 4, 13)
put_number(2, 5, 2, 10)
put_number(2, 5, 3, 40)
put_number(2, 5, 4, 65)
put_number(2, 5, 5, 40)
put_number(2, 6, 2, 15)
put_number(2, 6, 3, 80)
put_number(2, 6, 4, 195)
put_number(2, 6, 5, 240)
put_number(2, 6, 6, 121)
put_number(2, 7, 2, 21)
put_number(2, 7, 3, 140)
put_number(2, 7, 4, 455)
put_number(2, 7, 5, 840)
put_number(2, 7, 6, 847)
put_number(2, 7, 7, 364)
put_number(3, 3, 3, 1)
put_number(3, 4, 3, 4)
put_number(3, 4, 4, 11)
put_number(3, 5, 3, 10)
put_number(3, 5, 4, 55)
put_number(3, 5, 5, 90)
put_number(3, 6, 3, 20)
put_number(3, 6, 4, 165)
put_number(3, 6, 5, 540)
put_number(3, 6, 6, 670)
put_number(3, 7, 3, 35)
put_number(3, 7, 4, 385)
put_number(3, 7, 5, 1890)
put_number(3, 7, 6, 4690)
put_number(3, 7, 7, 4811)
put_number(4, 4, 4, 1)
put_number(4, 5, 4, 5)
put_number(4, 5, 5, 26)
put_number(4, 6, 4, 15)
put_number(4, 6, 5, 156)
put_number(4, 6, 6, 480)
put_number(4, 7, 4, 35)
put_number(4, 7, 5, 546)
put_number(4, 7, 6, 3360)
put_number(4, 7, 7, 7870)
put_number(5, 5, 5, 1)
put_number(5, 6, 5, 6)
put_number(5, 6, 6, 57)
put_number(5, 7, 5, 21)
put_number(5, 7, 6, 399)
put_number(5, 7, 7, 2247)
put_number(6, 6, 6, 1)
put_number(6, 7, 6, 7)
put_number(6, 7, 7, 120)
put_number(7, 7, 7, 1)
}
//////////////////////////// show
union{
object{Numbers}
object{Squares}
translate -<4, 4, 4>
}
// povray pyramid_liana.pov +ua +fn +W2000 +H1960
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Subcategories
This category has the following 5 subcategories, out of 5 total.
Pages in category "Number pyramid Liana (image set)"
The following 2 pages are in this category, out of 2 total.
Media in category "Number pyramid Liana (image set)"
This category contains only the following file.
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Number pyramid Liana.png 2,000 × 1,960; 243 KB