A fractal is a graph based on quantum physics. It echoes the real world in that although each dot on the graph is placed randomly under a certain set of conditions, they add up to a regular pattern.
A fractal generator is simply a program that allows you to create fractals.
Time depends on quite a lot - in the default mode, Apophysis provides 50 randomly generated fractals, which can then be altered. Alternatively, you can start from scratch, choosing all the details of the graph yourself. Picking a randomly generated image out of the 50 might take a few minutes, then a few minutes more to alter it, then a few more minutes (depending on size and quality) for it to calculate the final render. Starting from scratch, depending on how much practice you've had and whether you've got something specific in mind, could take anywhere from two minutes to an hour.
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