Wikipedia has this to say:
A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"a property called self-similarity. Roots of mathematical interest in fractals can be traced back to the late 19th Century; however, the term "fractal" was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
This image is one of the first that I toyed with. It has a fractal background with a digital photo of a white daisy inserted and manipulated. I use free fractal design software to create the fractals posted on my blogs. Fascinating and easy to use, Apophysis and Fractal Explorer are my favorites. Since I've given up dusting and such, free time is far easier to find.
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