More fractals

[Ross Younger]

- Collatz fractal

- julia, see also http://mrob.com/pub/muency/orbitbasedoptimization.html
  - set up a click/drag to move the julia point.

- Negative powers of Mandelbrot i.e. z->z^-2+c et seq
- Higher powers of the 'Misc' fractal set
- Try out Lyapunov exponent based colouring - see http://en.wikipedia.org/wiki/Multibrot_set#Rendering_images
- Try out orbit trap based colouring - see http://en.wikipedia.org/wiki/Orbit_trap
- newton fractal (newton's method?)
- investigate secant method
- Buddhabrot (though it could be difficult to make fit into the current model). For a good description see https://benedikt-bitterli.me/buddhabrot/
- Check out what http://www.chillheimer.de/kallesfraktaler/ has

Lambda. start = (0.5,0) exp = (2,0) eqn = c * z * (1-z)

Mandelbrot with imaginary powers(?!)

possible bubble mandelbrot:
z := z - ((z^4-z)/(4*z^3-1)) + c
z := z - ((z^3-z)/(3*z^2-1)) + c
z := z - ((z^2-z)/(2*z-1)) + c
z := z - (z^3-1)/(3z^2) + c

"seapods" z := z - (z^4-z^2-1)/(3z^3)

"islands" z:=(z-(z^3-1)/(3z^2))^3z

"swirly" z := z^2+c+0.5
"swirly2" z := z^2-c-0.5

another variation z := (z+0.5)/z^2 + c

z := z^3 - cz + c - 1

[Ross Younger (crazyscot)]

mandeldrop, bubblebrot and sinister are worth looking into - http://www.relativitybook.com/CoolStuff/erkfractals.html - if I can find formulae for them.

[Ross Younger (crazyscot)]

mandeldrop is the "inverse" mandelbrot. one site (without picture) describes it as mapping z0 to 1/z0.
bubblebrot is apparently similar but I haven't been able to track down a formula (yet?).

[Ross Younger (crazyscot)]

Formulas from fractint that look interesting, if I can figure out how to read them: spider, lambdafn, mandelfn.
Long-term we might want to think about a formula-based system like fractint, i.e. separate the fractal maths from the coding but at the likely cost of optimisation.

[Ross Younger (crazyscot)]

OK, we've done mandeldrop and its derivatives; haven't been able to find formulas for bubblebrot and sinister. More rapid experimentation will be needed to find them efficiently, which is current at the epic/blueprint stage and aiming for a later series.

[Ross Younger (crazyscot)]

Burning Ship, Variant, Generalised Celtic and Bird Of Prey added to gamma.

[Ross Younger (crazyscot)]

Tentatively targetting this for delta primarily as a follow-on from 872722.