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julia fractal

julia fractal

Interesting relationship between Mandelbrot and Julia fractals

4y ago


For each point in the famous Mandelbrot fractal, there is a unique Julia fractal. This video (made using the Mandelbrot Maps web applet - demonstrates an interesting relationship between the two. Moving back and forth along the main cardioid of the Mandelbrot (the large, heart-shaped bulb), the associated Julia fractal squeezes into an intricate pattern of bulbs, before breaking apart outside the borders of the Mandelbrot. Zooming in on the smaller cardioids of the Mandelbrot fractal, we can see the pattern repeat itself on a smaller scale at multiple points in the Julia fractals. If you'd like to further explore the Mandelbrot and Julia sets in real-time, Mandelbrot Maps has now been ported to Android, as part of my undergraduate honours project. You can find it on the Google Play Store - If you do use it, please leave a rating or a review and, if you have a few minutes to spare, fill out the usability survey linked in the app's description. This would be tremendously helpful for my dissertation. Mandelbrot Maps is open-source software. The source code for each version can be found by following its respective link above.