Mandelbrot mishaps

In the thread RC2014. A retro Cray? we see a distorted Mandelbrot:

I’ve seen that before, and was able to figure out what had gone wrong:

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I wish I could replicate an error that I made around age 16 when coding Mandelbrot: I made some error in expanding the formula, and the resulting fractal was wild: no more symmetric at all, but whirling spiky knots. Probably somewhat more like Julia sets. Lost the code years ago, sadly.

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We can has mandelbrot mishaps thread plz?

I once had a mishap in my fixedpoint maths and that fed a strange “noise” into the calculation.

[email protected]: The output of the corrected program.

As if by magic, we’ve transported to just such a thing. When @hoglet and I were working on his fork of DSPFract, which uses a Beeb-attached FPGA board to implement a Mandelmachine, we had some difficulty fine-tuning the hardware-optimised multiplications. We ended up with some empirical settings which I never quite got to grips with on a theoretical level. (It turns out that complex multiplication needs fewer multiplies than you’d think, and that squaring can be cheaper than general multiplication, and that you can make a 35 bit engine using slightly fewer 18x18 hardware multipliers if you synthesise some assistance logic. But there were some artefacts at extreme zoom which didn’t look right.)

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