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Logistic map graffiti – Dale Street, Manchester, 6.5.2019. en.wikipedia.org/wiki/Logistic_mapPermalink On twitter.com
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import matplotlib.pyplot as plt, numpy as np lmap=lambda x,r: r*x*(1-x) pts=2000 iters=1000 r=np.linspace(0,4,pts) x0=np.random.rand(pts) for i in range(iters): x0=list(map(lmap,x0,r)) plt.scatter(r,x0,0.1) plt.xlabel('$r$') plt.ylabel('$x_{%d}$' % pts) plt.savefig('map.pdf')Permalink On twitter.com
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(There was a typo in the above: plt.ylabel('$x_{%d}$' % pts) should have been plt.ylabel('$x_{%d}$' % iters) –but then it wouldn't have fit in a tweet 🤷) Anyway here's one coloured by the period of the cycle at each r, up to a maximum of 128. This one doesn't fit in a tweet 😅.Permalink On twitter.com
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Last go, for now. I realised the plot can be made to look nicer, and denser, by including all the points in each cycle, not just the last iteration. So here's the result of that, with 5000 points. Even with my terrible code, it runs in just a couple of minutes on my old MacBook.Permalink On twitter.com
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I put the code for these explorations into a Jupyter notebook and it's viewable here: mybinder.org/v2/git/https%3A%2F%2Fversion.helsinki.fi%2Fweir%2Fexploring-the-logistic-map/master?filepath=Logistic%20Map.ipynbPermalink On twitter.com
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The repo with this notebook is here version.helsinki.fi/weir/exploring-the-logistic-map/ and I tidied up the code to make the 'period plot'. I also fixed some problems that came up when actually trying to run the code on mybinder 😅 (namely, it needs a requirements.txt).On twitter.com
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