Gaël Varoquaux

Tue 27 January 2009

←Home

Error in my article

There is an error in a code example in my article that just came out in Linux Magazine France. I am so ashamed. I did test the code, but I didn’t have automated tests, so I broke it when tweaking it :(. I think the lesson is that you need to do more than doc-testing articles (it was doc-tested).

The code example is about calculating the Mandebrot set. The idea is that you take a grid of the numbers c complex plane, and iterate on it the function f = lambda z: z**2 + c. You look at the divergence of this iteration, and plotting a mesure of the divergence gives you a nice figure. The code I wrote was:

from numpy import ogrid, zeros, abs, isnan, ones
c = x + y * 1j
threshold_time = zeros((500, 500))
z = zeros((500, 500))
mask = ones((500, 500), dtype=bool)
for i in range(50):
    z[mask] = z[mask]**2 + c[mask]
    mask = (abs(z) > 10)
    threshold_time += mask

The error is subtle. First there is the not so subtle mask error: I am masking the points that diverge, and iterate them even further. This is exactly the opposite that I meant to do. Then there is the more subtle bug: the line “z[mask] = z[mask]**2 + c[mask]” is an in-place assignment. As a result the dtype of z is not modified: z is not magically cast in a complex. Thus the imaginary information coming from c is lost. And that information is crucial to Mandelbrot.

The right code is:

from numpy import ogrid, zeros, abs, isnan, ones, complex
c = x + y * 1j
threshold_time = zeros((500, 500))
z = zeros((500, 500), complex)
mask = ones((500, 500), dtype=bool)
for i in range(50):
    z[mask] = z[mask]**2 + c[mask]
    mask = (abs(z) < 10)
    threshold_time += mask

Plot the threshold_time array with pylab.imshow (from the matlplotlib project) to get a nice figure.

Go Top
comments powered by Disqus