1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
```
#Import libraries for simulation
import tensorflow as tf
import numpy as np
#Imports for visualization
import PIL.Image
from cStringIO import StringIO
from IPython.display import clear_output, Image, display
import scipy.ndimage as nd
```
```
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 = StringIO()
PIL.Image.fromarray(a).save(f, fmt)
display(Image(data=f.getvalue()))
```
```
sess = tf.InteractiveSession()
```
Exception AssertionError: AssertionError() in <bound method InteractiveSession.__del__ of <tensorflow.python.client.session.InteractiveSession object at 0x6247390>> ignored
```
# Use NumPy to create a 2D array of complex numbers on [-2,2]x[-2,2]
Y, X = np.mgrid[-1.3:1.3:0.005, -2:1:0.005]
Z = X+1j*Y
```
```
xs = tf.constant(Z.astype("complex64"))
zs = tf.Variable(xs)
ns = tf.Variable(tf.zeros_like(xs, "float32"))
```
```
tf.InitializeAllVariables().run()
```
```
# Compute the new values of z: z^2 + x
zs_ = zs*zs + xs
# Have we diverged with this new value?
not_diverged = tf.complex_abs(zs_) < 4
# Operation to update the zs and the iteration count.
#t
# Note: We keep computing zs after they diverge! This
# is very wasteful! There are better, if a little
# less simple, ways to do this.
#
step = tf.group(
zs.assign(zs_),
ns.assign_add(tf.cast(not_diverged, "float32"))
)
```
```
for i in range(200): step.run()
```
```
DisplayFractal(ns.eval())
```
```
```
|
