Workshop 202012 #4

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Another low-iteration non-fractal.

Warning, nerd talk follows. You may notice a discontinuity running up and right from the center. The underlying formula is this sequence of operations:

z = sin(z.re)+i*sin(z.im)+c\\z = a*z + b\\z = z^{0.9+i*0.1}

z and c have the usual meaning, a and b are parameters. In this case

a = -1.0 + i*1.1\\b=0.0+i*0.1

The first two lines are quite simple. If only the first two lines are used the resulting images are mildly interesting, but also forgettable. If we made the exponent in the third line 1.0, then it is just the identity function z = z, and basically we have just the top two lines.

The exponent in this case is, 0.9+i*0.1, is close to 1.0. It adds a little bit a spice, a little twist to the two-line set.

Complex exponentiation is not, in general, a continuous function. It is a multi-value function. That is an oxymoron since normally a function is defined as something that returns a single value. We define a proper function by picking one of the possible values. There is no way to pick values so that the resulting function is continuous.

So, adding the third line makes the picture more interesting, is also introduces the discontinuity.

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