Rozuvan Circles Fractal

I decided to use Jupyter Notebook to render a particular configuration of a generalized Mandelbrot set. The resulting fractal image is unique - i.e. I have not seen such a fractal before. I will be investigating whether this is trully something new, or if this has been done before. For now though, I call this fractal the Rozuvan Circles Fractal = )

Download ipynb file of this notebook.

See part 2 for the continuation of this work.

PS: More on the generalized Mandelbrot set later. Follow the discussion along at FractalForums thread.

import numpy as np

from pylab import imshow, show

import math

from timeit import default_timer as timer

def fractal(x, y, max_iters):
  """
    Given the real and imaginary parts of a complex number,
    determine if it is a candidate for membership in the fractal
    set given a fixed number of iterations.
  """
  c = complex(x, y)
  cL = abs(c)

  try:
    t2 = complex(cL, 10.0)
  except OverflowError, err:
    return max_iters
  try:
    t3 = pow(complex(-100.0, -2.0 * cL), c)
  except OverflowError, err:
    return max_iters
  try:
    t4 = complex(0.0, cL)
  except OverflowError, err:
    return max_iters
  try:
    t5 = complex(-200.0, -cL) * c
  except OverflowError, err:
    return max_iters

  z = 0.0j
  for i in range(max_iters):
    try:
        t1 = complex(cL, -10.0) + z
    except OverflowError, err:
        return max_iters

    try:
        T1 = pow(t1, t2)
    except OverflowError, err:
        return max_iters
    try:
        T2 = T1 + t3
    except OverflowError, err:
        return max_iters
    try:
        T3 = T2 + t5
    except OverflowError, err:
        return max_iters
    try:
        T4 = pow(T3, t4)
    except OverflowError, err:
        return max_iters

    z = T4
    if (z.real*z.real + z.imag*z.imag) >= 400000.0:
      return i

  return max_iters

def create_fractal(min_x, max_x, min_y, max_y, image, iters):
  height = image.shape[0]
  width = image.shape[1]

  pixel_size_x = (max_x - min_x) / width
  pixel_size_y = (max_y - min_y) / height

  for x in range(width):
    real = min_x + x * pixel_size_x
    for y in range(height):
      imag = min_y + y * pixel_size_y

      escape_num = fractal(real, imag, iters)

      if (escape_num == iters):
        image[y, x] = 255
      else:
        image[y, x] = 0

image = np.zeros((1080, 1920, 3), dtype = np.uint8)
start = timer()
create_fractal(-228.24, 228.24, -120.96, 120.96, image, 50)
dt = timer() - start

print "Fractal generated in %f s" % dt
imshow(image, origin='lower', extent=(-228.24, 228.24, -120.96, 120.96))
show()

Fractal generated in 46.978858 s

image = np.zeros((1080, 1920, 3), dtype = np.uint8)
start = timer()
create_fractal(-19.20, 19.20, -10.80, 10.80, image, 50)
dt = timer() - start

print "Fractal generated in %f s" % dt
imshow(image, origin='lower', extent=(-19.20, 19.20, -10.80, 10.80))
show()

Fractal generated in 109.465202 s

image = np.zeros((1080, 1920, 3), dtype = np.uint8)
start = timer()
create_fractal(-4.0, -4.0 + 80.0 / 9.0, 4.0, 9.0, image, 50)
dt = timer() - start

print "Fractal generated in %f s" % dt
imshow(image, origin='lower', extent=(-4.0, -4.0 + 80.0 / 9.0, 4.0, 9.0))
show()

Fractal generated in 88.165300 s

About this Jupyter Notebook

Server Information:

You are using Jupyter notebook.

The version of the notebook server is 4.2.1 and is running on:

Python 2.7.12 |Anaconda 4.1.1 (64-bit)| (default, Jun 29 2016, 11:07:13) [MSC v.1500 64 bit (AMD64)]

Current Kernel Information:

Python 2.7.12 |Anaconda 4.1.1 (64-bit)| (default, Jun 29 2016, 11:07:13) [MSC v.1500 64 bit (AMD64)]
Type "copyright", "credits" or "license" for more information.

IPython 4.2.0 -- An enhanced Interactive Python.
?         -> Introduction and overview of IPython's features.
%quickref -> Quick reference.
help      -> Python's own help system.
object?   -> Details about 'object', use 'object??' for extra details.

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© 2016 Valera Rozuvan. Fork me at GitHub.