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    <p>I worked from Lauritz V. Thaulow's code and was able to get a pretty significant speed-up with the following code:</p> <pre><code>import numpy as np import matplotlib.pyplot as plt from itertools import count def newton_fractal(xmin, xmax, ymin, ymax, xres, yres): yarr, xarr = np.meshgrid(np.linspace(xmin, xmax, xres), \ np.linspace(ymin, ymax, yres) * 1j) arr = yarr + xarr ydim, xdim = arr.shape arr = arr.flatten() f = np.poly1d([1,0,0,-1]) # x^3 - 1 fp = np.polyder(f) counts = np.zeros(shape=arr.shape) unconverged = np.ones(shape=arr.shape, dtype=bool) indices = np.arange(len(arr)) for i in count(): f_g = f(arr[unconverged]) new_unconverged = np.abs(f_g) &gt; 0.00001 counts[indices[unconverged][~new_unconverged]] = i if not np.any(new_unconverged): return counts.reshape((ydim, xdim)) unconverged[unconverged] = new_unconverged arr[unconverged] -= f_g[new_unconverged] / fp(arr[unconverged]) N = 1000 pic = newton_fractal(-10, 10, -10, 10, N, N) plt.imshow(pic) plt.show() </code></pre> <p>For N=1000, I get a time of 11.1 seconds using Lauritz's code and a time of 1.7 seconds using this code. </p> <p>There are two main speed-ups here. First, I used meshgrid to speed-up the creation of the numpy array of input values. This is actually a pretty significant part of the speed-up when N=1000.</p> <p>The second speed-up comes from only doing calculations on the unconverged portions. Lauritz was using masked arrays for this before realizing that they were slowing things down. I haven't looked at them in quite some time, but I do remember masked arrays being a source of slowness in the past. I believe it is because they are largely implemented in pure Python over a numpy array rather than being written almost completely in C like numpy arrays.</p>
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    1. POHow do I speed up fractal generation with numpy arrays?
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    1. USJustin Peel
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    1. POHow do I speed up fractal generation with numpy arrays?
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    1. COThanks to both of you!
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      1. USmrKelley
    2. COAmazing. Thank you for teaching me lots of new tricks. +1!
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      1. USLauritz V. Thaulow
 

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