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Fractal Witchcraft    

Robert P. Munafo, 2023 Jun 20.

Fractal Witchcraft is a DOS demoware program by David and Steven Stoft, notable for being the first implementation of a perturbation method, specifically the synchronous orbit algorithm. It also aimed to compete with FRACTINT on speed and features. It has built-in help and a comparatively easy-to-learn user interface, and supports several fractal recurrence relations.

The program was developed in 1992 and announced that year in Amygdala.

Take a look at the file LITENING.PCX: "Lightning Strikes at Midnight". Time to compute: Fractal Magic 10 hrs 50 mins FractInt 25 hrs 50 mins Fractal WitchCraft 4 mins 35 secs    140 & 338 times faster!! Now that's WitchCraft !!

Here is a recreation of the demo image, complete with "ghosts" rising up from the bottom. (In the original image supplied with the program, the ghosts had "eyes" drawn in and some superimposed words):

-0.104977567388 + 0.927041363781 i @ 1.1734e-11
Generated in DEMZ with 1 thread in 10.3 sec

This location is in filaments off of a period-270 island, but far enough from it that the lowest-period islands in the actual view area have periods of 5000 or more (see my original description of my analysis in the Synchronous Orbit Algorithm article). The total number of iterations needed for the image is only about 7000. This makes the area ideal for calculating quickly by patch iteration.


Fractal Witchcraft inspired improved patch iteration techniques (discussed in that article) including the open-source AlmondBread.


By 1999 the limitations of patch iteration were understood to be too great to be of use to most users, and hardware had not yet reached the point that extended precision was practical. Discussing his program FractalForge, Uberto Barbini wrote:

Now (December 1999) the situation is very similar. Fractal Witchcraft has been abandoned and no other program uses its algorithm.

This state of affairs changed some years later with the cubic deltas and other extrapolation-based methods.

revisions: 20230618 first version; 20230619 analysis of demo image, adaptations, legacy; 20230620 author names

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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