Hi Fred, “The Elven Palace” is indeed a 2D perspective view of a 3D ray-step render using a slightly brute force distance estimation method. It’s actually part of the standard quaternionic Mandelbrot for q^7+c but with an extra twist, if you take the quaternionic form is (x,y,z,w) then prior to calculating q^7 the (y,z) part is treated as a complex and rotated to 7* its original angle i.e. no change of magnitude. I was surprised when such a simple idea produced results very similar to the White/Nylander Mandelbulbs. Although similar to those Triplex Mandelbulbs (especially since here the 4th dimension, w, is zero throughout) it is not the same and seems to have less “whipped cream”, be more hollow and have fewer of the difficult tapering to infinitely thin sections found in the centre of the star shapes on the original Mandelbulbs of the same degree. Given that numeric adjustment (the extra twist) can someone more mathematically aware then myself possibly tell me how to calculate the derivative ? e.g. I’m guessing just use 7*q^6 where q^6 is quaternionic but with the twist first at *6 and the multiplication 7*(q^6) is purely quaternionic since both the y and z terms are zero for a simple real…...
On 1 Jan 2019, at 01:43, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I couldn't decode what fractal you were exploring in "The Elven Palace", but had the impression of an intriguing 3-space structure, though the rendering does not quite succeed in resolving any ambiguity. Have you investigated the practicality of a fly-through movie? WFL