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Science Forum Index » Fractals Science Forum » mandelbrots generated with skewed complex-number rules
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| jellovirus |
 Posted: Sat Feb 02, 2008 6:15 am |
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Guest
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I was writing a fractal generator, and just for the heck of it, I
decided to screw with the multiplication rule for complex numbers. I
was quite amazed at what I got. From far off, the image looks much more
chaotic than regular mandelbrots, and changes to the seed seem to change
the image more. But it produced many different kinds of images, all
self-symmetrical and all very beautiful. I've posted the code and a
link to some images generated with this method. I've not seen any like
this before, but if anybody has seen this before, I'd like to know about it.
http://www.photoblog.com/screamingcactus/2008/01/25/warped-plane-mandels.html
Other than the changes you see below, the rest of the code is exactly
like a regular mandelbrot test.
zr = z.real;
zi = z.imag;
z.real = zr * zr - zr * zi + c.real;
z.imag = zi * zi + zr * zi + c.imag; |
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| Ron Croonenberg |
| Posted: Sun Feb 03, 2008 4:14 pm |
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How/where did you compute 'white hot heat' ?
(what's the center of the area ?)
jellovirus wrote:
Quote: I was writing a fractal generator, and just for the heck of it, I
decided to screw with the multiplication rule for complex numbers. I
was quite amazed at what I got. From far off, the image looks much more
chaotic than regular mandelbrots, and changes to the seed seem to change
the image more. But it produced many different kinds of images, all
self-symmetrical and all very beautiful. I've posted the code and a
link to some images generated with this method. I've not seen any like
this before, but if anybody has seen this before, I'd like to know about
it.
http://www.photoblog.com/screamingcactus/2008/01/25/warped-plane-mandels.html
Other than the changes you see below, the rest of the code is exactly
like a regular mandelbrot test.
zr = z.real;
zi = z.imag;
z.real = zr * zr - zr * zi + c.real;
z.imag = zi * zi + zr * zi + c.imag; |
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| Guest |
| Posted: Mon Feb 04, 2008 1:21 am |
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interesting images. You know, as long as there is non-linear terms on
the equations, you will get chaos (and most probably, fractals).
My two cents, another attempt to "symmetrice" a bit the equations:
z.x = zx*zy + c.x;
z.y = zy*zz + c.y;
z.z = zz*zx + c.z;
and produces this: http://rgba.scenesp.org/iq/fractals/f3d/experimental/exp_gfx02.htm
(far much boring that yours)
I wonder if, following your idea, I should not try
z.x = zx*zx - zy*zy - zz*zzz + c.x;
z.y = -zx*zx + zy*zy - zz*zzz + c.y;
z.z = -zx*zx - zy*zy + zz*zzz + c.z;
looks that the obvious extension. I will try it, thx for the
inspiration ;)
Inigo Quilez |
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| Guest |
| Posted: Tue Feb 05, 2008 5:14 am |
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On Feb 2, 9:15 pm, jellovirus <static_r...@yahoo.com> wrote:
I've posted the code and a link to some images generated with this
method. I've not seen any like
Quote: this before, but if anybody has seen this before, I'd like to know about it.
Hi, I've rendered distorted Mandelbrot images using a formula similar
to that one before, that gave similar results (but nothing as cool as
that awesome "White Hot Heat" image of yours):
http://www.enzedblue.com/Fractals/Fractals.html
See "Black & White 11", & "Mandelplasma 1 & 2" especially. The
distortion formula is described at the bottom of the page. |
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| Roger Bagula |
| Posted: Fri Feb 08, 2008 11:07 am |
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Guest
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jellovirus wrote:
Quote: I was writing a fractal generator, and just for the heck of it, I
decided to screw with the multiplication rule for complex numbers. I
was quite amazed at what I got. From far off, the image looks much
more chaotic than regular mandelbrots, and changes to the seed seem to
change the image more. But it produced many different kinds of
images, all self-symmetrical and all very beautiful. I've posted the
code and a link to some images generated with this method. I've not
seen any like this before, but if anybody has seen this before, I'd
like to know about it.
http://www.photoblog.com/screamingcactus/2008/01/25/warped-plane-mandels.html
Other than the changes you see below, the rest of the code is exactly
like a regular mandelbrot test.
zr = z.real;
zi = z.imag;
z.real = zr * zr - zr * zi + c.real;
z.imag = zi * zi + zr * zi + c.imag;
There is a long line of this kind of "conformal" mapping
fractal. The investigation of something called "measure theory"
on the complex plane leads to some strange fractals.
Fuzzy Logic gives different "measures" like this.
Specifically:
zr = z.real;
zi = z.imag;
z.real = zr * zr + zi * zi-2*zr*zi + c.real;
z.imag =2* zr * zi + c.imag;
The one that Clifford Pickover did a long time ago is ( as I remember it):
zr = z.real;
zi = z.imag;
z.real = Abs[zr ]+ c.real;
z.imag = Abs[zi] + c.imag;
As I rember this one trurns out better:
zr = z.real;
zi = z.imag;
z.real = Abs[zr ]^2+ c.real;
z.imag = Abs[zi]^2 + c.imag;
Fractint in it's documentation has a list of these that are "built in".
Roger Bagula |
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