Image of the Week #170

A conjugate Mandelbrot set, rich in spirals.

IOTW

 

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Humans and Computers Collaborating on Art

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Occupy Math works with digital evolution on a number of projects including evolving parameters that generate interesting fractals. The advantage to doing this with a computer, assuming you can come up with an automatic function that at least sort of measures “this looks good”, is that you can sort through billions of fractals per hour. One of these is shown at the top of the page. The disadvantage is that people are much better than any of the automatic functions we have found so far at spotting cool fractals. If we use people, though, they burn out way before looking a even a paltry million fractals. This is the phenomenon of user fatigue. This post is about a way to let computers and people collaborate on a project, drawing on the strengths of each. Computers can evaluate huge numbers of fractals to find ones that might look good. Humans have a much better ability to judge which fractals are actually beautiful.

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Summer Math

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This post is themed “look at the pretty pictures”, with an attempt to make summer appropriate pictures. It is a look at some of the things that math can do. The secret for making Mandelbrot sets look like bouquets of leaves is featured. This is something that Occupy Math discovered by accident, a nice example of when a code bug is really a feature. The Mandelbrot set is an excellent source of complex pictures. The Ghost Mandelbrot set shows how you can switch up the details and get new fractals. In this post we will apply quadrant convergence to the Mandelbrot set and use a green color scheme to get leafy-looking fractals.

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