POV-Ray : Newsgroups : povray.binaries.images : Re: The Cubic Mandelbrot [23 kb] : Re: The Cubic Mandelbrot [23 kb] Server Time
8 Aug 2024 14:24:24 EDT (-0400)
  Re: The Cubic Mandelbrot [23 kb]  
From: Mike Williams
Date: 15 Jun 2005 16:26:11
Message: <6$VdAAAb7IsCFw2x@econym.demon.co.uk>
Wasn't it Orchid XP v2 who wrote:
>>>Also of interest: slice the isosurface and stick a matching 2D plot on
>>>the cross-section! (I will do this later if I figure out pigment
>>>functions...)
>> 
>> 
>> Here are cross sections through the three axes. I used 12 iterations here
>> (pigment functions are a lot faster than 3d isosurfaces).
>
>Neat!
>
>The bottom image looks like one would expect. The other two look like I 
>maybe messed up my maths somewhere... they don't look right somehow.
>
>The bottom image I'm guessing is A=(0, 0), B=(x, y). That looks correct. 
>If you try A=(x, y), B=(0, 0) it should look like this:
>
>http://www.felicite-parmentier.freeserve.co.uk/large/cubic-mand.gif
>
>However, it looks like the second image is trying to be that, but messed 
>up. Looks like I need to go recheck my math! (You'll notice that the 
>image that looks right doesn't use A at all - and there's an 
>optimisation involved with the A variable. Wanna bet I optimised it wrong?)
>
>Anyways, usually when rendered 2D, the part of the isosurface that's 
>solid is coloured black, and the parts outside are multicoloured. ;-) Of 
>course, there's no *law* about that...
>
>I'll go see if I can figure out if/where my code is wrong. :-S


I suspect that it has something to do with the values of T1 and T2.

When A=(0,0), T1=0 and T2=0, and the whole thing behaves exactly like a
conventional 2D cubic Mandlebrot (z = z^3 + #pixel as they say in an
UltraFractal script).

-- 
Mike Williams
Gentleman of Leisure


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