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Author Topic: Shattered fractal a LogicTurtle  (Read 2015 times)
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Alef
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Posts: 1174



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« on: April 03, 2013, 03:39:11 PM »

Conditional / discontinuous formulas don't seems being popular, but here I tryed something barnsley like. Maybe an another attempt on bicycle, but hadn't noticed simmilar things. Fractured pieces and julia sets seems to be loosely related to mandelbrot set, and it uproaches point (0,1) like mandelbrot set.


Here is optimised code:

float cabsz=cabs(z)  ;complex modulus of z
float cabsc=cabs(c)  ;complex modulus of c

IF (cabsz < cabsc)
z= (z)^@power - c
ELSEIF (cabsz == cabsc)
z= (z)^@power
ELSE
z= (z)^@power + c
ENDIF

It have nice holed julias starting with power 4 and interesting shattered mset insides just next to the border when using inside colouring. Made a few fast non-pretencious images, most of even without antialiasing.











This is mandelbrot inside just next to the bprder and coloured with direct (point) orbit traps.


« Last Edit: April 07, 2013, 05:26:03 PM by Alef » Logged

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Alef
Fractal Supremo
*****
Posts: 1174



WWW
« Reply #1 on: April 03, 2013, 03:42:48 PM »

And example spot of Ultra Fractal. Named this LogicTurtle as it is based on logical operation and consists of pieces.

Code:
LogicT_Mount_Flora {
::53PAqhn2lNVTPuNIQ07RK/HQ+eTw4gtTr4wGpurUV3eIal2jRTw4YawgFGvJ5ffHsjT/6GMv
  5j384RtHkBw85lLIkgOYUikv7Oplvd4V3gNc4ZjzDJkL6qQjYTJl0o0naCiscKxA3U+eRasW
  pXVpD9ikn6rg2vsZdxaGNNLZ5ixsG7vE6CanVksDknP5x+XlQcdgUHuJSpUSwD2+OwrsBxNV
  /yFtQXn2eaqaMqyLorYssyy8s8iy0t58yN810VcWWBNPtgx4Z8stFb4kW4kVslySL2mltcRt
  z3OYgxW1CX1xexxZ2p8yGl8swVXTq1GlFaRRQ1uaouNhgD1fbWTG8oAlE7Q3hjg24GCRejN5
  Qn7C2QGeqXFC36UiXBblyc07CxgX0BZzM03GMaYqN/MeEXqMcJyx73p5fXdksY0guzoVVCrb
  q25wY5UOp+Q9gViEpPI0VIvjZY/Q5D3LRb7x4Tv0RhuGJs1ZVLXg7x/DZ0WF4/HJRaeIJvDf
  oezrlNeX7so0BGcFxcfeyWR+61O0Ap8Ej+sKZUdQ2gvX4Rn/Y0x8jRKQeIS73hsCvJdmWVox
  VhjSHaIyofU5jNxChBPY09qHaRctrRrV+nIPJjWlBIoI7fZXMfT0yuHHbRcKSwA+5bjQvISX
  xuzhR0xAzo7ieO+DsprLXcyDVacQjqWfrzhfQQTLRjPcXFUkv4mLKLSzZll3jGN5TxTzTZpl
  c+dAGlO6xHx2kz3meHI73VwzxXqpfL/5MRxaekz/lYckf/CVg9jS
}
« Last Edit: April 07, 2013, 05:25:32 PM by Alef » Logged

fractal catalisator
Alef
Fractal Supremo
*****
Posts: 1174



WWW
« Reply #2 on: April 07, 2013, 05:23:37 PM »

In post above signs were wrong, with opposite signs escape time version have the shape as its orbit map (buddhabrot). This should be right even if it coresponds to non canonical z=z^2-c mandelbrot set:

IF (cabs(z) < cabs(c))
z= (z)^@power + c
ELSEIF (cabs(z) == cabs(c))
z= (z)^@power
ELSE
z= (z)^@power - c
ENDIF

This fractal have interesting properties. It consists of broken pieces of finite elements, jet it is fully conformal on zooming, moreso than say tricorn fractal. Alsou it don't detiorates with higher powers as say burning ship. It looks almoust as being universal. Maybe it represents something.

It have julia sets like of mandelbrot, but consisting of finite blocks.


Deltoids corresponds to antenna region of mandelbrot.


Black pieces are insides, they are non- connected and of finite size but forms a self -simmilar network.



Here is Escher's Relativity version of elephant valley.



Julia set. Not a something unseen before, but very slowly escaping, >1000 iterations on x11 zoom.


Orbit maps aka buddhabrot with region corresponding to escape time fractal inside coloured blue and outsides red.
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