Burning Ship variant

[lkmitch]

Hi all,

I developed a new formula, which is a variation on the Burning Ship formula.  Recall that the standard Mandelbrot (& Julia) formula iterates:

z = z^n + c

and the Burning Ship iterates:

z = (|re(z)| + i*|im(z)|)^n + c.

My thought originally was to split the power n into a "burning" part and a "non-burning" part, so

z = z^n_non_burn * (|re(z)| + i*|im(z)|)^n_burn + c,

so the effective power n = n_non_burn + n_bun.  No reason to stop there, so I broke it down into four parts:

z = z^n_non_burn * (|re(z)| + i*im(z))^n_burn_x * (re(z) +i*|im(z)|)^n_burn_y * (|re(z)| + i*|im(z)|)^n_burn + c.

This formula allows you to set four independent exponents.  Depending on how they are set, the image will have features of the Burning Ship fractal, features of the standard Mandelbrot (or Julia), or completely different features.

If you use Ultra Fractal, then I put this formula (Burning Ship 4, Mandelbrot and Julia versions) into the formula database.  Here are a couple of example images.

[vinecius]

Nice find, a lot of liquidy plasma effect in these like in the pic.  Would be interesting to see it animated, seeing the spikes loop into each other

[greentexas]

Good job! These fractals are nice. I've played around with them, and I enjoy seeing the symmetry. I believed simon.snake already discovered this formula until you mentioned the four exponents.