Hmmm... you can recalculate a formula 1000 times but you'll get the same answer 1000 times. The key is that this formula is reiterated, meaning that the result of the formula calculation is input back into itself and the formula recalculated. This can be done as often as wished. The answers derived from these calculations are used to plot the fractal image which is essentially nothing more than a graph, albeit often a very beautiful graph. The fractal formula is often exceedingly simple yet can be the source of extremely complex imagery. These patterns are without limit so can be enlarged endlessly, each enlargement showing more and more detail. Fractals show similar detail at various enlargements, referred to as fractal scaling. Many fractals are also self-similar. As you dive into (enlarge) a fractal image the pattern may disappear only to reappear in various guises as you continue to dive. The degree and frequency of self-similarity may vary from formula to formula. The foregoing is extremely simplistic. Mandelbrot, discoverer of the formula bearing his name, defined fractals in terms of the mathematics used to calculate fractal dimensions. He later expressed regret for having done so, preferring to leave the definition of fractal open. Curiously, within the context of fractals as art what we call a "fractal" is not the actual fractal. Rather, it is a visual representation of the effects of the fractal on surrounding geometric space and determined by how the artist has chosen to colour such effects. - Jack