#!/usr/bin/env python

# 2017-02-12 Simple Mandelbrot / Julia set example
# http://algoristo.com/teaching/

import math

nsteps = 500

maxiter = 100

# Squared
limit = 4.0

# Floats
xmin = -2.0
xmax = 1.0
ymin = -1.5
ymax = 1.5

# Julia set only
#cx, cy = 0, 1

datfile = open("heatmap.dat", "w")

for i in range(nsteps + 1):
    for j in range(nsteps + 1):
        x = xmin + i*(xmax - xmin)/nsteps
        y = ymin + j*(ymax - ymin)/nsteps

        # Julia
        zx, zy = x, y
        
        # Mandelbrot
        #zx, zy = 0, 0

        for n in range(maxiter):
            # Note both components at once
            zx, zy = zx**2 - zy**2 + x, 2*zx*zy + y

            # Wrong order is also interesting
            #zx = zx**2 - zy**2 + x
            #zy = 2*zx*zy + y
            
            if zx**2 + zy**2 > limit:
                break

        # Note: starting point x, y, not the result
        datfile.write("%f %f %f\n" % (x, y, n))

datfile.close()