## About Fractals and their Slide Shows

**What is a Fractal?**

A geometric figure or natural object that combines the following characteristics:-

a) Its parts have the same essential form or structure as the whole, except that they are at a different scale and may be slightly deformed. Thus "Fractal Repetition" of pattern and shape.

b) Its form is extremely irregular or fragmented, and remains so, whatever the scale of examination. Consider the leaf of the fern as a good example.

c) It contains "distinct elements" whose scales are almost infinitely varied and cover a large range.

Any shape that has the unusual property that when you measure its length, area, surface area or volume in discrete finite units, the measured value increases without finite limit as the size of the discrete unit decreases to zero. The oldest standard example is a coastline ("How long is the coast of Britain?"), which when measured one kilometer at a time might turn out to be 5000 kilometers long, but when measured just one meter at a time comes out to be, say, 12000 kilometers. Measured per centimeter, would further increase the distance!

Generation of fractal images employs the useage of mathematical expressions, these often being trigonometrical in type, or polynomials and quadratics - containing numerous adjustable variables. There is then performed a sequence of many iterations during which the shapes are ''built'' and colors are introduced by further math' and color filters - these in fact giving a large degree of control to the finished image form, and not just color.

A most useful feature is that zooming in to portions of the original will yield repeated patterns at ever increasing magnifications (almost infinite), during which ''discovery'' of particular image forms can be made, often with no small amount of excitement! Many forms begin as symmetrical and many are presented here as such - however "exploring" into deep corners often reveals hidden delights where symmetry ceases to play as big a part. Sometimes an opportunity presents, such that two or even three ''versions'' can be made - possibly just a color change can alter the image meaning.

All the work you will see (Fractal Extravaganza 1 and Fractal Extravaganza 2) has been achieved with quite an old software application called "TIERAZON" - a very versatile package, and quite the best we have found - permutations are in effect all but infinite. Sometimes an image then goes through extra stages such as rotation, cropping, color adjustments, resizing and even on a few, addition of extra graphic elements, to tell a new story. We have titled the ones we show here, just for amusement, although sometimes the image content suggests a title very easily.

All fractal images are © *copyright ACB Systems* and not to be reproduced without permission. Please email us at with any requests (please, no spam) ..... plus for most images we have larger versions available at modest cost, usually big enough to print to 17" x 13" nominal or its inverse, sometimes larger. Note - the slide show images are of necessity not only reduced in dimension but also quite heavily compressed to around 50k file size, this in order to reduce download times and so reduce slowing of the slide sequence too much. Quality loss is actually quite modest. A fast connection is desirable but for dial-up users, once the images are "down" they should be cached - making for easier re-runs though a presentation.

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