Title: Radius and angle-factors seperated
Post by: Krumel on August 21, 2010, 12:34:46 AM
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:
 \cdot a \cdot i} \cdot abs(z)^r)
Where a is the angle-factor and r is the ratio-factor.
The angle-factor does determine how many blobs you get:
(http://npshare.de/files/c2981365/angle1to4.png)
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:
(http://npshare.de/files/e7043758/mandel_a6_r1.3.png)
a = 6; r = 1.3
If you decrease the angle-radius-ratio you'll get a bloblike appearance:
(http://npshare.de/files/834177dc/mandel_a2_r5.png)
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 (http://npshare.de/files/e40b0b16/map.png), but beware: It's 3mb big.
Edit: Corrected link.
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:
(http://npshare.de/files/c2981365/angle1to4.png)
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:
(http://npshare.de/files/e7043758/mandel_a6_r1.3.png)
a = 6; r = 1.3
If you decrease the angle-radius-ratio you'll get a bloblike appearance:
(http://npshare.de/files/834177dc/mandel_a2_r5.png)
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 (http://npshare.de/files/e40b0b16/map.png), but beware: It's 3mb big.
Edit: Corrected link.
Title: Re: Radius and angle-factors seperated
Post by: cKleinhuis on August 21, 2010, 02:36:58 AM
very interesting the correct link to the map is:
http://www.npshare.de/files/e40b0b16/map.png
http://www.npshare.de/files/e40b0b16/map.png
Title: Re: Radius and angle-factors seperated
Post by: kram1032 on August 21, 2010, 04:35:43 PM
nice stuff :)