“Burning Ship” fractal

Glad to see Paul Bourke is still active. I encountered his site almost 20 years ago and spent many hours on it. Fantastic stuff. Glad to see he still maintains a minimalist site.

I used to spend a ton of time in the Xaos program poking around the Burning Ship. You could middle-click and it would make a Julia set based on the point you clicked, and you could find some amazing stuff in the rigging of the ship.

This fractal is non-holomorphic which makes it kind of a dumpster fire..or a burning ship I guess... The easiest layman's definition of holomorphic is any function or operations on complex numbers that doesn't peek at the real and imaginary parts of the complex number. In algebra, there is no combination of algebraic operations [1] that can do so. But on computers, we have Re(z) and Im(z), which are easy to calculate since the complex number is simply stored as two parts, and it just pulls one of them out.

When you violate this sacred notion, of treating a complex number as a singular entity, indivisible, the operations or functions you get, no longer have nice properties, like being analytic [2]. You are no longer doing algebra, you have gone into the realm of chaotics over R^2 with an equivalence relation through rotations, which is a far different beast.

That's why other fractals that treat complex numbers as first class citizens, singular entities, and don't use hacks like Re or Im, are much prettier and have less branch cuts.

[1] https://en.wikipedia.org/wiki/Algebraic_operation

[2] https://en.wikipedia.org/wiki/Analytic_function

Incredibly creepy. What if one day we found a fractal that contains a message from God?