## What are Fractals?

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

a) Its parts have the same form or structure as the whole, except that they are at a different scale and may be slightly deformed.

b) Its form is extremely irregular or fragmented, and remains so, whatever the scale of examination.

c) it contains "distinct elements" whose scales are very 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 basically employs the useage of mathematical expressions, these often being trigonometrical in type, or polynomials and quadratics - containing several adjustable variables. There is then performed a sequence of iterations during which the shapes are ''built'' and colors are introduced by further math' filters.

The most useful feature is that zooming in to portions of the original will yield repeated patterns at ever increasing magnifications, during which ''discovery'' of particular image forms can be made.

A word on the image content. Sometimes an opportunity presents, such that two or even three ''versions'' can be made. Sometimes just a color change alters the image meaning, or even a background addition. Much is based also on geometric symmetry - a common feature of many fractals.

I offer this collection as simply an exploration, voyage if you will - into the realms of fractal imaging.  Enjoy the stunning shapes and often vibrant colors. Go to the Gallery start page one now to start your tour.

(NOTE - the images are reduced from large versions and so do suffer some slight loss of quality.)