Title: Kaleidoscopic Patterns Generator Post by: Kali 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= } Title: Re: Kaleidoscopic Patterns Generator Post by: Kali 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= } Title: Re: Kaleidoscopic Patterns Generator Post by: Alef 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 Title: Re: Kaleidoscopic Patterns Generator Post by: Kali 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, |