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Author Topic: Kaleidoscopic Patterns Generator  (Read 2535 times)
Description: Simple implementation in UF5
0 Members and 1 Guest are viewing this topic.
Kali
Fractal Supremo
*****
Posts: 1138


« on: May 20, 2011, 07:46:47 AM »

Hi, I want to share this formula I just made. Is for generating and trying to understand how kaleidoscopic patterns works.

The parameters are:

Translation - just like Julia values, and geometrically represents linear movement.
Rotation - In degrees, positive or negative
Scale - Scaling of coordinates (use values >1 or <-1)
Power - Raises Z to a power (use negative for inversion)
Fold - Abs function, aplied to real, imag or both

Default values shows a variant of the classic "kaleidoscopic tree".

The signs of translation, scaling and rotation are important in order to get any results.
Translations values set to 0,0 sets Mandelbrot mode (useful only with powers > 1 and < -1) you can use then eyedropper to get Julia values.

Exponential smoothing of magnitude is included as coloring method.

Hope you like it!

mostro {
::2UR0Vhn2dJ12OuNIQ03jU+HQ8+6gvvpV8SV7jVqS5DIaWD2mGgBBYtJ9rvTszmeRySAjnzl5
  AjRYID2PtfHjlNZrWydYKHRO7djKPLLFCBbWbmmzyOarFupjJZ5dADRtykTS+Pg3s4nbPUJo
  vyS++drtty6AEyG0L5fBGuMFxFvizwAMYy3uzOzpzzoS6WsZTASp97cQIY8Tbw1+sOKfRU0U
  VX/aVffT5BRhQ01XXLKP2ycwkXWW0IaO203xA/ENFHF73NiRiUYlGHc1cnnaBLojDz6hLScc
  kNasaP40PmhqilRH/OAS24NJ/CY1GFZ3Mh2n4sw5fKFFtHIeODymWahSjiaaNgvvlLhzjoVJ
  nxo5Xoni397M+kRp3i5I4TjkXGWeTHRM//moYZwy/wAf7a4kjaamCkvjK+G/pByXks0UiL5n
  Ur0kMUsKKK/jMWjXDx/SkTZwrgo6f05r6RguBI+nigyQV3if05o90d8JjLY1M6v3WVn9RfFc
  Wa1hyb6ELiZY9++lmum27UY8K91tjEdWMKFPr18sWZXfffVJh4xbjV5fQsHfgQ88lTVL16vB
  Sh93yB==
}

Pablo2.ufm:kaleidopatterns {
::05ZQOhn21FZUrNMIUU43F8/gk9SSaoLZdFGdTI/SGcbqZ1iRFjZLI5H/0U7qM28l45457ylT
  4Su9AG1pG0C2MRTfQznZi7Od0aMyR1YEvns0eZhGMIE/DePmYkFVtX8S5JePGhRClSfYFptX
  JOdjxRNMQk7K2AHHz5DwH+7FlN8rT6e8mY8QsISxmY+/I+TJxdF/sHOqrkNrzb4la+jNvUX2
  CFr2v3qVfV2OupLstHBuQNF6hXXcLv1G1Yk1MxCBOx6hJRIwAMztMDdXdSpBGYgcpi0BaLXJ
  pZWDIHFQQkVRi0086t7rqLqI+1blBj6FKwGHAkMAjy+b6n3/fgjJgjdgglQ1sd3/h5bgEQvi
  ZSBTxuCE661i2fuFr+mBTONQzOrMcnSaBRGJ7Tmxy7WveUZP7/IVSW26vn4gxovBzZPxBC==
}

Pablo.ucl:ExpSmoothingMod {
::zb/yagn2l9YTONMMQU49Wy3hRpbSAVodLSRqStcC4EM04AjkjHTmJShR9wjdbRsgFez7nv3Y
  vjSk+i3BwYkRFMD6hdPt7PFR+nyy0vSeXk5cpvZ9yXza7lN2lOvrEpv8eMsmb3u/Z8dp1sti
  0V9kezqVHpEGvuNAbo0QYtgtC/B4gcGjhaohwIuEvdiKpxQJTzrrZOFSKhR4tJm1Pp0HQ7EP
  sEXkumaRAy4MOB3JVH5MmViTVCH5IPDnCJh0vbuZffqi9+6fLkGuSw7+Bo4rUlD=
}


* treesample.jpg (83.71 KB, 500x300 - viewed 987 times.)
« Last Edit: May 20, 2011, 02:57:31 PM by Kali » Logged

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Kali
Fractal Supremo
*****
Posts: 1138


« Reply #1 on: May 26, 2011, 04:24:41 AM »

This is the same but with bailout condition

mostro {
::APjk2jn2NKZTOuNMMU49BI3BBtPOyuxJFtQbGMHgCMHgAGLab1IJKIJjZ8tv0/0gusAeBl4j
  f8RR3nguC4+xxDCRxWcoW6pcJRSxnWTZUXrUKxIaHGL6rcoDmxUWXvUQXCN2SWL/F8wR/s9c
  D/pqrlHPsKblaHELWKolvBdPHS0UwIFUE6sl5F6CPWGJj2P5K2IkzHP4hY0GG2KHDFMpVnZh
  wQYpx9UiFDrp9wX2l8fTJiYqbE7eqp+eRv1hBwj7erpaq3LXKgxlm1yngDtG2GFu6QWKi3/t
  +kq6656qL8BQfhJePrPtdOSfuNzx7PArjmK66mvzn6JnR/gKjHPYDZrBXtlB5Ye+UVtiSCC5
  e2jObAh0/YtPKQwAJT1UnT+Xn9O2D8TBbWuJvA+CSgC4/PihEYs8tbPlk3zx8+6DrP6QBndO
  3BbRr6qkisn4pRPjZRiKw6u7Udb7CBbwgfpv0yocUSXf92tbN1t73voaPjid/2Ketz7MD0uS
  1rfAaWA/HkYVQ/J=
}

Pablo2.ufm:kaleidopatterns {
::mlS42hn21FZ0qNMIUY47F8dQyupJN0lsuOGdTIPJDON1saxoixsFk8wPN1uKjVvR//9/7whz
  hL529YUrqXLYTEN9BNfiJu50SrwIHVjR8Oycz5ZawgQ8f49YiBWU1c2LlH5dYEGJUK9+FkmO
  l44VGH1wAxKX+a4wwKeP8p/deRN/SluFvOGPELikvOm/fi/UScX+v9hj6KYT6V18CN/x6XrK
  ag8F7Pa0qvLaGW3G62DAXoGDzhZ387NRJG9m1MyCBOy6gRRIQPMxtMDdbVyQDMQP5cJpF0Wu
  SSzsGQOIggIrkEpprq2srsKvk4bvFGMqToAbsAQSBMK7fpfe39AHSAHaBBLhqez27h5nAJge
  FzkCePs40JBN6kC/SK9FuwmaZN5PXzVd1gJH7pZnUGuTJtgIjk9FzY5tLPPosn8XSlkltscj
  FGj+Bwf+aPA=
}
Logged

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Alef
Fractal Supremo
*****
Posts: 1174



WWW
« Reply #2 on: April 12, 2012, 04:16:46 PM »

I think, you should upload this to UF database.

Exponent smoothing could be improvement by adding some number befor modulus. Sometimes it generates nice effects and sometimes allows fine tune the fractal:

zz=sqrt(|#z + @SomeNumber |)
sum=sum+exp(-1/abs(zz-ss))
ss=zz

 
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fractal catalisator
Kali
Fractal Supremo
*****
Posts: 1138


« Reply #3 on: April 12, 2012, 06:31:26 PM »

I'm about to finish a set of formulas and coloring algorithms that I'll upload to the UF database.

Thanks for the tip

Cheers,
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