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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > IFS - Iterated Function Systems > Amazing Box, Amazing Surf and variations > Continuous Conformal Mandelbrots
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Author Topic: Continuous Conformal Mandelbrots  (Read 19948 times)
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fractalrebel
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« Reply #15 on: February 22, 2010, 03:36:25 AM »
Last one for tonight. This is a rotation of the Conformal Julia with the Stone Face. In this case we get a Cathedral.

* ConformalCathedral.jpg (180.91 KB, 640x640 - viewed 521 times.)
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kram1032
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« Reply #16 on: February 22, 2010, 03:16:34 PM »
wow, that stone face is creepy!
Great cheesy

A 3D-print anyone? smiley
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fractalrebel
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« Reply #17 on: February 24, 2010, 02:07:20 AM »
I had to keep playing with these formulas. I added the inversion code to the Conformal code, set up options to do the Box, Rotate and Inversion operations in any order, and set up a loop so that the set of operations could be performed 1, 2, ... times per iteration (the default for Conformal is 2). I am still testing and tweaking the code, but this interesting image, which I call Courtyard Ruins popped out. It uses a loop count of 2 and an operation order of Rotate Box Invert.

* CourtyardRuins.jpg (165.07 KB, 640x640 - viewed 458 times.)
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cKleinhuis
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« Reply #18 on: February 24, 2010, 02:20:11 AM »
i played around with the unity function

ORIGINAL FRACTINT CODE:

Code:

unity {
init:
  float ddelmin = 2 / (#magn * #width)
  float x = 0
  float y = 0
  float one = 0
  z = pixel
  
loop:
  x = real(z)
  y = imag(z)
  one = |z|
  y = (2 - one) * x
  x = (2 - one) * y
  z = x + flip(y)
  
bailout:
  (one <= 2.0) && (abs(one - 1) >= ddelmin)

default:
  title = "Unity"
  maxiter = 149
}

this is easily extendable to 3d:

length=length(triplex)
triplex.x=(2-length)*triplex.z
triplex.y=(2-length)*triplex.x
triplex.z=(2-length)*triplex.y

normal bailout/iteration method as in standard mandelbrot

have not rendered it yet, just examined 2d slices of it :

* Clipboard03.jpg (4.49 KB, 625x410 - viewed 601 times.)

* Clipboard05.jpg (4.99 KB, 623x419 - viewed 432 times.)
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Timeroot
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« Reply #19 on: February 24, 2010, 05:57:26 AM »
Tglad, that wouldn't give quite the same thing, since |z| here doesn't mean length(), but rather length()^2. Did you remember to include this fact when drawing it? wink
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cKleinhuis
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« Reply #20 on: February 24, 2010, 10:29:34 AM »
oh, no, have to correct it cheesy
i always mix it, i have adjusted the formula and rendered some more slices

it isa surely not as interesting as the amazing fractal, but it could make a nice seashell object

* test2.jpg (103.55 KB, 1903x998 - viewed 613 times.)

* test3.jpg (98.88 KB, 1885x998 - viewed 467 times.)
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divide and conquer - iterate and rule - chaos is No random!
ericruijun
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« Reply #21 on: September 11, 2012, 01:16:06 PM »
What Software do you use when making those?huh?huh?. I tried lots of softwares, but they all suck
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