The 4‑Dimensional Mandelbrot Object

Description

These 6 views are generated using the six different settings of the python script, ‑tA, ‑tB, ‑tC, ‑tD, ‑tM and ‑tJ. Each letter defines a plane where two of the 4 positional parameters (zx,xy,cx,cy) are kept fixed and two are varied. The Mandelbrot set exists in a plane where zx and zy are fixed and cx and cy are varied. The Mandelbrot image ('M' below) has been anotated to show the two C axes, cx (green) and cy (yellow).

The Julia sets exist on the planes where the values of cx and cy are fixed, and the initial Z value, (zx,zy) is allowed to vary. In the Julia image 'J' the zx axis is highlighted in red and the zy axis in magenta.

You can now see how the 6 planes intersect by matching up the corresponding coloured axes. The Julia and Mandelbrot planes have no common axis as in 4 dimensional space it is possible for two planes to intersect at a single point. In these examples, that point is (0,−1,0,0).

If you pick three axes and find the three views based on these axes you can imaging slotting them together and creating a 3‑dimensional slice of the 4D object. It is hard to imagine the whole 4D entity.