Renders colorful density plots of the roots of polynomials with coefficients drawn from a small set of sets.

polynomial-root-phase-diagram.py

import numpy as np
import cv2
import itertools
import math
import cmath

w = h = 1024
deg = 11

# The root phases to sample frame, and the color that goes with each.
n = 60
col_samp = [(
    cmath.exp(1j*math.pi*k/n),
    np.array([math.cos(k*math.pi/n*2), math.cos(k*math.pi/n*2+1),math.cos(k*math.pi/n*2+2)])) for k in range(n+1)[1:]]

# Iterate over all polynomials with coefficients limited to 1 or root phase up to a desired degree.
# Dump a density plot of their roots into dat, with colors.
dat = np.array([[[0.0, 0.0, 0.0] for i in range(w)] for j in range(h)])
for p, c in col_samp:
  print(p)
  for coefs in itertools.product([1, p], repeat=deg):
    for r in np.roots([1] + list(coefs)):
      x = math.floor(r.real * (w/5.0) + (w/2))
      y = math.floor(r.imag * (h/5.0) + (h/2))
      if x >= 0 and x < w and y >= 0 and y < h:
        dat[y, x, :] += c

# Temp copy for easier re-processing when in the REPL
dat2 = dat*1.0

dat = dat2*1.0
dat = np.abs(dat)
dat *= 25
dat = ((dat > 50)*(math.log(dat/50.0) + 50.0)) + (dat <= 50)*dat

img = np.array(dat, np.uint8)
cv2.imshow('image', img)
cv2.waitKey(0)
cv2.destroyAllWindows()