Prime factorisation diagram

primes.py

# -*- coding: utf-8 -*-
#
# Author: Vegard Nossum <[email protected]>

import math
import os
import sys

import cairo

w = 7
h = 7

# https://stackoverflow.com/a/22808285/1697183
def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors

def fours(n):
    factors = []
    while n % 4 == 0:
        factors.append(4)
        n //= 4

    return factors + prime_factors(n)

# https://math.stackexchange.com/a/1806107/179367
def r(n):
    s = math.sin(math.pi / n)
    return s / (s + 1)

out_w, out_h = 128 * w, 128 * h

surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, out_w, out_h)
cr = cairo.Context(surface)

cr.set_line_width(0)
cr.set_source_rgb(1, 1, 1)
cr.rectangle(0, 0, out_w, out_h)
cr.fill()

def draw(factors):
    if not factors:
        cr.arc(0.0, 0.0, 1.0, 0.0, 2.0 * math.pi)
        cr.fill()
        return

    n = factors[0]

    if n == 4:
        cr.rotate(-math.pi / 4)
    for i in range(n):
        cr.save()
        cr.rotate(2.0 * math.pi * i / n)

        cr.translate(1.0, 0)

        cr.scale(0.95 * r(n), 0.95 * r(n))

        draw(factors[1:])
        cr.restore()

cr.set_source_rgba(.5, 0, 0, 1)
for y in range(h):
    for x in range(w):
        cr.save()
        cr.translate(1. * (.5 + x) * out_w / w, 1. * (.5 + y) * out_h / h)
        cr.scale(28.0, 28.0)
        cr.rotate(-math.pi / 2)

        number = 1 + y * w + x
        factors = list(reversed(fours(number)))
        draw(factors)

        cr.restore()

surface.write_to_png('output.png')

Output: