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Fractals

Although it is intended that in time these pages will embrace a wide spectrum of all matters fractal, their primary purpose is to reveal some amazing fractals that were discovered in the escape-time diagrams generated by the chaotic dualist formulæ of fuzzy logic.

The escape-time diagrams can be thought of as a series of overlapping planes or layers contained within a fractal boundary. Each succeeding plane has been tiled with an identical motif, wherein the tiles are not only smaller in area by half but also their orientations are rotated by 45° from the plane above. (Is this what is meant by 'twisting the truth'?)


boundary boundary boundary
fig(i) escape-time diagrams showing top, third and fourth layers and relative orientation

boundary
fig(ii) escape-time diagram showing fractal tiling

The tile motifs can be formed from a wide variety of shapes and segements of those shapes giving rise to sometimes beautiful but more often odd looking diagrams. Occasionally where the tiles overlap a second set of fractal boundaries can be discerned and it is these that have also attracted interest.
boundary
fig(iii) escape-time diagram showing inner fractal tiling

As more of these fascinating fractals are discovered they will be added to the page Fractal One.

The fractal pages, so far as they have been developed, also include programs that can reproduce the Mandelbrot Set, the Julia Set, and circular interference patterns...More yet to come

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