The Mandelbrot Set - Iteration by Iteration with Angles

The Mathemagicians' Guild Commons
The Mathemagicians' Guild Commons
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Published 2021-06-04
This animation is a variation of one I did on the Maths Town channel. It shows the Mandelbrot Set forming iteration by iteration from a radius 2 circle. It includes the angles of a polar grid, and domain colouring related to that angle. To draw the image, z is calculated for a point, then the original image is sampled for a colour.

Notice how at the end the angles in the cardioid align with the bulbs. Period 3 at 120 & 240. Period 4 with 90 & 270 (180 is period 2, also technically period 4). You also get zeros in each bulb (the colours meet) corresponding to the period of that bulb.

(This video has no audio)

   • The Mandelbrot Set - Iteration by Ite...   - 2nd Power Mandelbrot
   • 3rd Power Mandelbrot - Iteration by I...   - 3rd Power Mandelbrot
   • 4th Power Mandelbrot - Iteration by I...   - 4th Power Mandelbrot
   • 5th Power Mandelbrot - Iteration by I...   - 5th Power Mandelbrot
   • Mandelbar Tricorn - Iteration by Iter...   - Mandelbar/Tricorn
   • Burning Ship - Iteration by Iteration   - Burning Ship
   • Perpendicular Mandelbrot  - Iteration...   - Perpendicular Mandelbrot
   • Celtic Fractal - Iteration by Iteration   - Celtic Fractal
   • Buffalo Fractal - Iteration by Iteration   - Buffalo Fractal

This channel is a companion to "The Mathemagicians' Guild". Here I will release mathematical animations under a Creative Commons Attribution Licence. In the process of making those videos I end up creative lots of animations that I don’t publish, and I thought it might be nice to release them somewhere. So, I’ve created this channel. The animations will be on random topics and without narration. I also operate the “Maths Town” channel, so you might see some fractal stuff pop up here also.

youtube.com/c/themathemagiciansguild - The Mathemagicians' Guild
youtube.com/c/mathstown - Maths Town

Permission is granted to use these videos under the Creative Commons Attribution Licence. I’m happy if you just link back to the original video. Additionally, in an academic context you may use the videos or screenshots if you provide the appropriate credit or citation. Please check the description for the licence status of any audio (usually YouTube audio library, or creative commons).
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