The standard chromatic subdivision visualized

standard_chromatic.py

# The standard chromatic subdivision is a mathematical operator in combinatorial topology that takes a chromatic
# simplicial complex and subdivides in a fractal-like manner. It represents all states of a distributed system after
# processes participate in an immediate snapshot.

# Immediate snapshots are a theoretical synchronization primitive, equivalent to atomic registers up to computational
# equivalence. They are used extensivelty in computability proofs within the context of distributed computing.

# This code draws the third standard chromatic subdivision of the 2-simplex (vertices are not colored).

from tkinter import *
from operator import add
from math import sqrt

root = Tk()

frameWidth = 1200
frameHeight = 575
eps = 1./3

canvas = Canvas(root, width = frameWidth, height = frameHeight)
canvas.pack()

def plus(point1, point2):
        return list(map(add, point1, point2))

def mult(scalar, point):
        return list(map(lambda x: scalar * x, point))

def standardChromaticSubdivide(canvas, point1, point2, point3, level, lwidth):
        scs = lambda x, y, z: standardChromaticSubdivide(canvas, x, y, z, level - 1, lwidth/2.)

        # Generate points
        # Edges
        point12a = plus(mult((1 - eps)/2, point1), mult((1 + eps)/2, point2))
        point12b = plus(mult((1 + eps)/2, point1), mult((1 - eps)/2, point2))
        point23a = plus(mult((1 - eps)/2, point2), mult((1 + eps)/2, point3))
        point23b = plus(mult((1 + eps)/2, point2), mult((1 - eps)/2, point3))
        point31a = plus(mult((1 - eps)/2, point3), mult((1 + eps)/2, point1))
        point31b = plus(mult((1 + eps)/2, point3), mult((1 - eps)/2, point1))
        
         # Face
        point123a = plus(mult((1 - eps)/3, point1), plus(mult((1 + eps/2)/3, point2), mult((1 + eps/2)/3, point3)))
        point123b = plus(mult((1 - eps)/3, point2), plus(mult((1 + eps/2)/3, point3), mult((1 + eps/2)/3, point1)))
        point123c = plus(mult((1 - eps)/3, point3), plus(mult((1 + eps/2)/3, point1), mult((1 + eps/2)/3, point2)))

        # Draw edges
        canvas.create_line(point31a[0], point31a[1], point123b[0], point123b[1], width=lwidth)
        canvas.create_line(point31b[0], point31b[1], point123b[0], point123b[1], width=lwidth)
        canvas.create_line(point1[0], point1[1], point123b[0], point123b[1], width=lwidth)
        canvas.create_line(point1[0], point1[1], point123c[0], point123c[1], width=lwidth)
        canvas.create_line(point123b[0], point123b[1], point123c[0], point123c[1], width=lwidth)

        canvas.create_line(point12a[0], point12a[1], point123c[0], point123c[1], width=lwidth)
        canvas.create_line(point12b[0], point12b[1], point123c[0], point123c[1], width=lwidth)
        canvas.create_line(point2[0], point2[1], point123c[0], point123c[1], width=lwidth)
        canvas.create_line(point2[0], point2[1], point123a[0], point123a[1], width=lwidth)
        canvas.create_line(point123c[0], point123c[1], point123a[0], point123a[1], width=lwidth)

        canvas.create_line(point23a[0], point23a[1], point123a[0], point123a[1], width=lwidth)
        canvas.create_line(point23b[0], point23b[1], point123a[0], point123a[1], width=lwidth)
        canvas.create_line(point3[0], point3[1], point123a[0], point123a[1], width=lwidth)
        canvas.create_line(point3[0], point3[1], point123b[0], point123b[1], width=lwidth)
        canvas.create_line(point123a[0], point123a[1], point123b[0], point123b[1], width=lwidth)
if level <= 1:
                canvas.update()
                canvas.postscript(file="scs0.ps", colormode="color")
                return
        
        scs(point31a, point123b, point31b)
        scs(point12a, point123c, point12b)
        scs(point23a, point123a, point23b)
        
        scs(point1, point123b, point123c)
        scs(point2, point123c, point123a)
        scs(point3, point123a, point123b)
        
        scs(point123b, point1, point31a)
        scs(point123c, point2, point12a)
        scs(point123a, point3, point23a)

        scs(point123b, point3, point31b)
        scs(point123c, point1, point12b)
        scs(point123a, point2, point23b)
        
        scs(point123a, point123b, point123c)

scale = 450 # altitude
shift = [350, 10]
topwidth = 4
point1 = plus(shift, mult(scale, [1/sqrt(3), 0]))
point2 = plus(shift, mult(scale, [0, 1]))
point3 = plus(shift, mult(scale, [2/sqrt(3), 1]))
        
canvas.create_line(point1[0], point1[1], point2[0], point2[1], width=topwidth)
canvas.create_line(point2[0], point2[1], point3[0], point3[1], width=topwidth)
canvas.create_line(point3[0], point3[1], point1[0], point1[1], width=topwidth)
        
#canvas.update()
#canvas.postscript(file="scs0.ps", colormode="color")
        
input()
        
standardChromaticSubdivide(canvas, point1, point2, point3, 3, topwidth)
        
root.mainloop()