Radius and angle-factors seperated

[Krumel]

In the normal mandelbrot, the factors of the radius and the angle of z are always the same (i.e. with z^2 the angle of z gets doubled and the radius gets squared).

If you now seperate them and change them, you get quite interesting results.
So the formula now looks a bit like this:

Where a is the angle-factor and r is the ratio-factor.

The angle-factor does determine how many blobs you get:

In this image, I kept the angle-radius-ratio to one, so these are the normal multibrots from z^1 to z^4.

If you increase the angle-radius-ratio you'll get a starlike appearance:

a = 6; r = 1.3

If you decrease the angle-radius-ratio you'll get a bloblike appearance:

a = 2; r = 5

I've generated a map, where I've iterated from a = 1; r = 1 to a = 3.375; r = 3.375 in 0.125 steps.
The "main sequence" (where a = r) is bordered in green.
Get it here, but beware: It's 3mb big.

Edit: Corrected link.

[cKleinhuis]

very interesting the correct link to the map is:

http://www.npshare.de/files/e40b0b16/map.png

[kram1032]

nice stuff