Sequence Fractals Part V #24

405.jpg

z^{s_i}+c
si = 0.5, 2.5, … (repeating)
Center:-1.3322+0.1473i; Zoom = 128

Now back to the repeating two-step square root sequences. See Sequence Fractals Part V #10

The story so far: Several sequence fractal formulas with the sequence as an exponent have been examined. There are examples of positive integer, integer, rational, and irrational exponents. The pictures get messier and math value become more doubtful with this progression.

In the last few days I have been dissecting my imagined dichotomy of discovery vs construction. Rather there is a process: exploration, discovery, knowledge, tool, construction.

So I am just going to embrace it, and spend the rest of this series at various points along that process. Can these equations be used to create interesting abstract art? Can something be extracted that I can add to my toolbox? I am going to explore, with more interest in finding future potential, than producing a finished masterpiece.

For the simple case, two simple fractions. 1/2 and 5/2, repeating. It is possible to get some control over the formula. The result exhibits the mosaic appearance from the non-integer exponents, while retaining the fractal self-similarity.

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