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ENH: compute mask only once per iteration in fractals notebook #103

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Aug 23, 2021
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ENH: compute mask only once per iteration in fractals notebook #103

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31 changes: 18 additions & 13 deletions content/tutorial-plotting-fractals.md
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Original file line number Diff line number Diff line change
Expand Up @@ -198,10 +198,11 @@ def divergence_rate(mesh, num_iter=10, radius=2):
z = mesh.copy()
diverge_len = np.zeros(mesh.shape) # Keep tally of the number of iterations

# Iterate on element if and only if |element| < radius (Otherwise assume divergence)
for i in range(num_iter):
# Iterate on element if and only if |element| < radius (Otherwise assume divergence)
diverge_len[np.abs(z) < radius] += 1
z[np.abs(z) < radius] = f(z[np.abs(z) < radius])
conv_mask = np.abs(z) < radius
diverge_len[conv_mask] += 1
z[conv_mask] = f(z[conv_mask])

return diverge_len
```
Expand Down Expand Up @@ -252,8 +253,9 @@ def julia(mesh, c=-1, num_iter=10, radius=2):
diverge_len = np.zeros(z.shape)

for i in range(num_iter):
z[np.abs(z) < radius] = np.square(z[np.abs(z) < radius]) + c
diverge_len[np.abs(z) < radius] += 1
conv_mask = np.abs(z) < radius
z[conv_mask] = np.square(z[conv_mask]) + c
diverge_len[conv_mask] += 1

return diverge_len
```
Expand Down Expand Up @@ -325,8 +327,9 @@ def mandelbrot(mesh, num_iter=10, radius=2):
diverge_len = np.zeros(z.shape)

for i in range(num_iter):
z[np.abs(z) < radius] = np.square(z[np.abs(z) < radius]) + c[np.abs(z) < radius]
diverge_len[np.abs(z) < radius] += 1
conv_mask = np.abs(z) < radius
z[conv_mask] = np.square(z[conv_mask]) + c[conv_mask]
diverge_len[conv_mask] += 1

return diverge_len
```
Expand All @@ -349,8 +352,9 @@ def general_julia(mesh, c=-1, f=np.square, num_iter=100, radius=2):
diverge_len = np.zeros(z.shape)

for i in range(num_iter):
z[np.abs(z) < radius] = f(z[np.abs(z) < radius]) + c
diverge_len[np.abs(z) < radius] += 1
conv_mask = np.abs(z) < radius
z[conv_mask] = f(z[conv_mask]) + c
diverge_len[conv_mask] += 1

return diverge_len
```
Expand Down Expand Up @@ -391,10 +395,11 @@ def newton_fractal(mesh, f, df, num_iter=10, r=2):
diverge_len = np.zeros(z.shape)

for i in range(num_iter):
pz = f(z[np.abs(z) < r])
dp = df(z[np.abs(z) < r])
z[np.abs(z) < r] = z[np.abs(z) < r] - pz/dp
diverge_len[np.abs(z) < r] += 1
conv_mask = np.abs(z) < r
pz = f(z[conv_mask])
dp = df(z[conv_mask])
z[conv_mask] = z[conv_mask] - pz/dp
diverge_len[conv_mask] += 1

return diverge_len
```
Expand Down