Multi-set formula for mandelbrot and related abs-fractals.

[TheRedshiftRider]

I've been playing around with different mandelbrot sets today and I found a very simple formula to create several mandelbrot fractals in one image. Here are some examples:

http://imgur.com/a/1iRLl


This is the formula I used:

abs((1.8-abs(z^2))^2)+c

It is possible to use the absre and absim on both places. You can change the powers outside the ()'s. It is also possible to change the distance between the sets and also move around the ()'s around to change the effect of the abs-function.

These were just some examples but it is possible to create these sets:

-Normal mandelbrot of any power.

-Burning ships of any power.

-Buffalo's and celtic fractals of any power.

-Perpendicular fractals. (mandelbrot, burning ship, celtic, buffalo.)

-And mandelbar fractals of any power.

-Cubic quasi (perpendicular) fractals.

-And partial burning ship fractals.

-It is also possible to create hybrids.


As far as I know this formula can be used with any power. It is even possible to let sets ''grow'' together.