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I don't know how complex powers are calculated, but this are some formulas I've tried in UF5 with interesting results.

z = c ^ z * @m
z = c ^ z * @m + c
z = 1 / c ^ z * @m + 1 / c
(bailout above 1000)
Note: '@m' is a multiply factor entered as a parameter to modify the drawing, for example 1, 0.9, -0.7...


z = z ^ (0,2)  + c
z = z ^ (0,-2)  + c
(bailout above 10000)

They don't generate something as wonderful and with the great diversity of the original mandelbrot, but it's worth seeing, the images are very non-conventional fractals.

A few samples... I don't remember the exact formulas for each one, but they derivates from the above:

(http://sphotos.ak.fbcdn.net/hphotos-ak-snc6/hs075.snc6/168593_1715661861223_1528504553_1740104_6686896_n.jpg)

(http://sphotos.ak.fbcdn.net/hphotos-ak-snc6/hs034.snc6/166453_1715662421237_1528504553_1740106_2777118_n.jpg)

(http://sphotos.ak.fbcdn.net/hphotos-ak-snc6/hs058.snc6/168867_1710042280737_1528504553_1729704_6002606_n.jpg)


Pretty strange patterns, don't you think?

Kali, those pictures are very interesting, and I think I've done similar things, but I have a question about the notation everyone here seems to use.

What is the meaning of c? Is it a constant across all pixels, or does it vary by pixel? In other words, If I write z = z^2 + c, am I describing the Mandelbrot set or a Julia set?

Ken

I was talking about varying c by pixel like the M-Set, but I also tried the formulas like Julia sets with some good results.

Thanks for the clarification!

@ken, you describe a formula, if initial values come along you have the julia/mandelbrot distinguation
alone it can not be distinguished, usually people mean the mandelbrot method ( varying per pixel )
and the julia method is implied ( constant per pixel )

regards

Thanks, Christian.

Here are two simple Julia-type examples using complex exponents, colored with escape time.

(http://i1122.photobucket.com/albums/l540/Fractal_Ken/ComplexExponent1.png)
z = z^(0, 2) + (1.08, -0.50); Iterations = 75; Bailout = 10; The red is the non-escape region

(http://i1122.photobucket.com/albums/l540/Fractal_Ken/ComplexExponent2.png)
z = z^(0, -2) + (0, 0); Iterations = 1000; Bailout = 100

Nice! Here's another:

(http://img52.imageshack.us/img52/7016/juliacomplexpow.jpg)

z=z^(0,2)+(0.2330725,0.228134) - Iterations:100 - Bailout: 15000 - Location center: 0,0 - Standard zoom

Cool pic!

Here's a Mandelbrot-type image where I've zoomed into the interior, i.e, non-escape region. I believe the coloring method I've used is called an orbit trap. (I can provide details if anyone's interested.)

(http://i1122.photobucket.com/albums/l540/Fractal_Ken/ComplexExponent3.png)
z = z^(0.0, 0.5) + c; Iterations = 110; Rotated -90 degrees

I struggle with the notation and terminology folks use. The unrotated image is centered at (-0.9065, -0.2870), but I don't have a frame of reference to compute a zoom magnification. If it helps: x varies from -0.951 to -0.862, and y varies from -0.350 to -0.224.

As I mentioned I was using UF5, I mean with "standard zoom", the zoom the program has for default, without touching anything.
I guess the notation you used it's the right one...

Kali, I use software I wrote myself, and I'm unfamiliar with UF5's terminology. I certainly didn't mean to imply there's anything wrong with it. Perhaps someone else can provide a translation between the two ways of describing zoom.

Regards,
Ken

Anyway, besides UF5 terminology, just wanted to say "no zoom", or the zoom level that shows the whole mandelbrot set if using the standard formula... -2 to 2 on the real axis (x), I guess... I'm also don't know much about notations   :embarrass: