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Is this a new way of bringing the Mandelbrot set to life? Each number on the complex plane, c, is repeatedly squared to give a new value, and then added to the original value c. This gives a path for each c that takes it around the plane. Those that don’t run off to infinity are in the Mandelbrot set. This animation allows the c to move along its path, and colours the plane at the starting position c with the colour of the plane at the end of the path. The plane is coloured so it is black everywhere with a rainbow disk in the centre [so at time 0, when the points haven’t started moving, we just see the rainbow disk]. As time progresses, after a series of bifurcations and pulsing beats, we see the familiar Mandelbrot set take form. [interactive] [code] [more]

Is this a new way of bringing the Mandelbrot set to life? Each number on the complex plane, c, is repeatedly squared to give a new value, and then added to the original value c. This gives a path for each c that takes it around the plane. Those that don’t run off to infinity are in the Mandelbrot set. This animation allows the c to move along its path, and colours the plane at the starting position c with the colour of the plane at the end of the path. The plane is coloured so it is black everywhere with a rainbow disk in the centre [so at time 0, when the points haven’t started moving, we just see the rainbow disk]. As time progresses, after a series of bifurcations and pulsing beats, we see the familiar Mandelbrot set take form. [interactive] [code] [more]

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    mandelbrot set
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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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