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Description
People familiar with complex numbers and Taylor approximations might be able to guess what I've done here. I've taken the 13th-order Taylor series approximation for the sine wave, and multiplied it by i, and then added z or whatever you want to call the domain variable, resulting in this complex polynomial. The curve representing the range of the polynomial when only real numbers are supplied as a parameter actually looks like a basic graph of the 13th-order Taylor approximation I started with; that would be the middle of the five wavy curves. Anyway, the graph was limited in its V extents for purposes of clarity.
I'm strongly considering writing a new kind of fractal renderer, which takes a complex function and plots the density of its range. (New for me; this type of plot appears to be quite common in fractal art already.) Some brief experimentation with a complex polynomial grapher I'd already written resulted in this image, which I thought interesting enough to share here. I'll probably move this to scraps when I have a prettier render.
I'm strongly considering writing a new kind of fractal renderer, which takes a complex function and plots the density of its range. (New for me; this type of plot appears to be quite common in fractal art already.) Some brief experimentation with a complex polynomial grapher I'd already written resulted in this image, which I thought interesting enough to share here. I'll probably move this to scraps when I have a prettier render.
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852x556px 64.31 KB
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fourier and laplace transform are far more difficult