Editing Mandelbrot set (section)

===Higher dimensions===
There is no perfect extension of the Mandelbrot set into 3D, because there is no 3D analogue of the complex numbers for it to iterate on. There is an extension of the complex numbers into 4 dimensions, the [[quaternion]]s, that creates a perfect extension of the Mandelbrot set and the Julia sets into 4 dimensions.<ref name="javier-barrallo"/> These can then be either [[cross section (geometry)|cross-sectioned]] or [[Projection mapping|projected]] into a 3D structure. The quaternion (4-dimensional) Mandelbrot set is simply a [[solid of revolution]] of the 2-dimensional Mandelbrot set (in the j-k plane), and is therefore uninteresting to look at.<ref name="javier-barrallo">{{cite web|last=Barrallo|first=Javier|date=2010|title=Expanding the Mandelbrot Set into Higher Dimensions|url=https://archive.bridgesmathart.org/2010/bridges2010-247.pdf|access-date=15 September 2021|website=BridgesMathArt}}</ref> Taking a 3-dimensional cross section at <math>d = 0\ (q = a + bi +cj + dk)</math> results in a solid of revolution of the 2-dimensional Mandelbrot set around the real axis.{{Citation needed|date=July 2023}}