1. A method of generating fractals comprising the steps of: convolving generator patterns with seed patterns of dots to generate convolution results for each of a plurality of sample spaces, such spaces being consecutively ordinally numbered in order of their successively more sparse sampling; expanding the convolution results in each of the higher numbered sample spaces through interpolation to a sampling density comparable to that in a lower numbered sample space; combining samples of the convolution results and the expanded convolution results of similar sampling density on a corresponding sample-by-sample basis; and carrying out said steps of expanding through interpolation and said steps of combining so as to result in the expanded convolution results of each of the higher numbered sample spaces ultimately being combined with the convolution results in said first sample space, thereby generating said fractals.