It seems completely natural that going from 2d to 3d adds a new dimension of awesomeness to fractals. Accordingly, it is quite a shame that until very recently, I was not aware of the magnificent Mandelbulb. If this is a new world for you, too, go and explore the wonders of 3d fractals using tools like Mandelbulb 3d.
What about 4d now? Did you ever think fractals could be used in rendering art digitally? http://www.segmation.com
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In 4d, defining the analogues of the Mandelbulb fractal is somewhat more straightforward because we have a division algebra structure there in form of the quaternions. However, this seems to lead to much smoother, less fractal, fractals. Of course, fractals (2d/3d/4d/…) are a mainstay of digital art; see many examples on platforms like DeviantArt.
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