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#@title Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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Visualizing the Mandelbrot set doesn't have anything to do with machine learning, but it makes for a fun example of how one can use TensorFlow for general mathematics. This is actually a pretty naive implementation of the visualization, but it makes the point. (A more elaborate implementation may be provided down the line to produce more truly beautiful images.)
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# Import libraries for simulation
import tensorflow as tf
assert tf.__version__.startswith('2')
import numpy as np
# Imports for visualization
import PIL.Image
from io import BytesIO
from IPython.display import clear_output, Image, display
Now you'll define a function to actually display the image once you have iteration counts.
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def DisplayFractal(a, fmt='jpeg'):
"""Display an array of iteration counts as a
colorful picture of a fractal."""
a_cyclic = (6.28*a/20.0).reshape(list(a.shape)+[1])
img = np.concatenate([10+20*np.cos(a_cyclic),
30+50*np.sin(a_cyclic),
155-80*np.cos(a_cyclic)], 2)
img[a==a.max()] = 0
a = img
a = np.uint8(np.clip(a, 0, 255))
f = BytesIO()
PIL.Image.fromarray(a).save(f, fmt)
display(Image(data=f.getvalue()))
It's handy that you can mix NumPy and TensorFlow.
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# Use NumPy to create a 2D array of complex numbers
Y, X = np.mgrid[-1.3:1.3:0.005, -2:1:0.005]
Z = X+1j*Y
Now you define and initialize TensorFlow tensors.
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xs = tf.constant(Z.astype(np.complex64))
zs = tf.Variable(xs)
not_diverged =tf.Variable(tf.zeros_like(xs, tf.bool))
ns = tf.Variable(tf.zeros_like(xs, tf.float32))
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for i in range(200):
# Compute the new values of z: z^2 + x
zs = zs*zs+xs
# Have we diverged with this new value?
not_diverged = tf.abs(zs) < 4
# Operation to update the iteration count.
#
# Note: We keep computing zs after they diverge! This
# is very wasteful! There are better, if a little
# less simple, ways to do this.
#
ns = ns + tf.cast( not_diverged, tf.float32)
Convert from tensor to numpy array for visualization
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ns = ns.numpy()
Let's see what you've got.
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DisplayFractal(ns)
Not bad!