For those who like their gnarl the old fashioned way I've uploaded a fractal formula version of Dynamical Systems. Find it in mt.ufm. There are far fewer parameters than the coloring algorithm. For info on that see here...
https://www.ultrafractal.com/forum/index.php?u=/topic/566/new-dynamical-systems-coloring-algorithm

I've also added four new dynamical systems functions to mt.ulb. Three are examples from Pickover's book Computers, Pattern, Chaos and Beauty. The other, called "Alternate", lets you load two functions and use them on alternate iterations.

For those who like their gnarl the old fashioned way I've uploaded a fractal formula version of Dynamical Systems. Find it in mt.ufm. There are far fewer parameters than the coloring algorithm. For info on that see here... https://www.ultrafractal.com/forum/index.php?u=/topic/566/new-dynamical-systems-coloring-algorithm I've also added four new dynamical systems functions to mt.ulb. Three are examples from Pickover's book _Computers, Pattern, Chaos and Beauty_. The other, called "Alternate", lets you load two functions and use them on alternate iterations.
 
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Here's a quick test run of this formula. This uses the CPCB Figure 14.14 plug-in.

5bd0b6d5a2fa5.jpg

DynamicalSystems2 {
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Sfd8dN3UdQNbxmZTmu/Lt1jXs5G9Zb+sFTHvu45b59Df465pnvve+27mue29xxwPP6HeFq//
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qOLGShLPcQSziuQywNby7TbQEEDnf0WqlwPcXA96hzvucsypC0ddB0nM7Gdax0FXPtHc3nM7
f6SmdRIybdHp9jFVsnL1OXqwD69OvkSp2c+xqeHqszJYBlSdBjx/UlfCPSP2emx+kh7ZQ0JD
R3JlU0TS2+aU/GdFEiYJWhZynktkS5In6vcKf3MSRapzBUxepA/jZFX9sLkCbJJZSXMmuunf
mxWxiYEqmLcOqK5pUrVdEXPX4I5kIPlPM5Z/6B9Zrwzh1DYhjVJWrmUtQ1Y4PdQR2KEadFWt
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uJqi/2nUqN1xGrUPWuPsTfyC7EaDsk38Xgkq4YsE7sJNuhySB3yOEylIQwmQ7hAnKYWswxby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}

Here's a quick test run of this formula. This uses the CPCB Figure 14.14 plug-in. ![5bd0b6d5a2fa5.jpg](serve/attachment&path=5bd0b6d5a2fa5.jpg) DynamicalSystems2 { ::Q8xTQjn2t3VTztxNS07uK/fgluLK0o/AAZLeIJblNHWXJVtpSt7l1FjIlEjpI5SStr9/+tB5 MAgiYsJdUckdmL2jwwBDmh4hX3vubwbWP+6tjn/Vv8FDGsd225THdxf9dLGf/srHP/f8uNbn e/G7FD+fzms9uRgxSDub6sbvb7In4HMf87muezIMetXve6kZb3M6ifY72lDe14bfYzfBMXZp rsGwfxLfxuP8ubz1jXtd2yFju4bGf9bud9yHWM5iBLXN+6ZbfnePMDuf66bne/yJTHtZ82HW PO+pf5Luf8qVzWc7+uY6itTXP6SYoD8O+KYI64B3P+2FjMDNB9Pe5LuZ567fY+4df+7H/2Zx LwaGczs5T1nP958+tDf4m7vYg2XrfX8PvcS7T+lb2/ofR8iX9670elE2C6xTeY88XfzDLuOO q2Maxy9fk/53pN9jjXP++9d88f5re1P96v9H/2v51f3sbfY9UgGC0FH8JHuaX/6s0++4fVtP Sfd8dN3UdQNbxmZTmu/Lt1jXs5G9Zb+sFTHvu45b59Df465pnvve+27mue29xxwPP6HeFq// KYEclZ/dflNec8As9Aq5gXNyO0y6Bjn8r6VM0s/QrO8txL+mXfzCYkOiWs9lvY5Dbf+O4ud9 4Jz0j2N62c/yl6063NdzgZLmM9tjMDue58lrHBWvNYCummJXqdLJWD30OY3N6aOXwRMGaPlP 02O78oPQNnwqH1cCDaCEB6bs9z9LHTLWmGStIDLzxx/yHWdIK6vFbagtLIkiB2Ob183NY6bX NW7yJNTZnFnfPK+EUBZ+3jNNAgu60l/3pr1LTbZ7dLn0cPGvZTVUqR/aqBa2Fscwqprv+upX /mRLv5miZJ/6qDgorm92pz/1VdAAWscx0Dn+pfnvJO4NDhipiLvt75h/0032uijtB8fj++Qf 39v3ND6i9zLvECDFkvyjDt2Qz8TLPkc4VXCyQwjNzbX+/iP2eyF2/Xxplsx69NzlHycwH2Pf 2M0TeivSXCjcOXTPwjohMBu4xyIeox6iz2X5GdpZozw+d/lPuYoeKJe5Wv4CNXeI+0rjVK2u Y3dv29SHoGox1j/lN7O0Oa74F7OCHN+6lbOZ4CZchgYbaGlm2Rvx5ttNDGoAtYCg3gpzpX8+ TIMaZL2iWAXGGRMsDQ3cK2nQlGCtULa1qvQ2fC9hVc682mhlJkv/BnSmBYaEDt9FIkghzDU2 NAi7kYT5LnuY/kyVjXrvijvX3jJ28m9H3T49US499f7X/8lw73vB3BIYdQ9GlAIig7EMjoYU oRTrSCkB6KTYB+T5IbOFTOQkExXLSm1lF8+Evn1nRfK5qxAcCYaTgcME0/p9EYLJqFBPEXRs Cqs8RoFsZyD/H3Uccnar4xRH3Fg68ouSrxB8BLAMoYAX03fEErdtuQ/aB9rF8pftAAZG5Q78 efy0V121QocxAqFpGwgLZfsPt6Bp03+QLdvlKNFgEwqTDaPnDyXESYykakbHWEb0Fcoze1Ad 8f0qBUo+qB1w96wuWrOojVDYzptag9zczsP5J6FWXj7nsD+mp4S0a2mJ3uR+hBjaK8VXaHiA wRjl3MVntCinQx1gPsZ4xQdCpztHioT9ZrgNwkdQC1I6m+2v790eYhat7dnsNuAbN+EUINXM Ydka0dicxVMxWtLVnnmmqlsLFQ9xIQJ0gvtzU7z1JNhypQtQOyZEj7JysUq3s0nP6w4eOrDj 7ZjZpeIIYLWiSMRKqUd8GLW62khsAEYLfEHF4inyncksEzikVCGfC/lYwQvTtAmPbSHiqwZo Dy4lX5El8R5BYNjQZfZX8eJYM9mb2jxf+jxJxgA3Otnbl+xBqJohSIut9KcseyCG2kKSevPp hEFK5k9q3buE+2iJPMFPTyZDvriNbEGuyJK8y0kHf1g3W83O8eeMUNK++PLy0u5/se7gx/ym 3jKtXCg+Xe7VXKhhBv7PTy0qvEYrr1fqkmnq9rgN5bm+pywFMEt7kSkTZZS9oY8JRfSB1wrG rjOfhMtUScHLrgbyckMtB9yNAl0Qhy3f2FU+9WxoUbAaRrWxwRFleSMHG7C/c3DT7tF+TCP5 +b2PP6ivX735bXuYwPtc9DtA5GWoPEv0+OpC10TJp5nyR65zgqkbxl6eUgYIhAqUuGIDK9kN kidC4ksUsgz7TicAcBJqe9exnuNGKR7SoFCnMJaBdncs0M79vvCJq74PsO+OqNdc9oO49sIQ 4sWDoH33j7fOh79WlENZHsLL0EFJk5ShazM1ERci1PAZjwZGSs3lZ4gCuFCzOgmjNrnFdRhP CcvjrIJL1BuPAVMe+YTyx9O0fik/wHMxJ+CW9V68Vf19Hi6rsevR5xivqfhJkHzqqU4pn3Jq RiYKBD4sLjeDhFS63eL4gNgl63bbvGBFkwnqkCoT5+vbz8xTm0bx5nOlZ+xlrue56FNzkP5l x/0pOzvvDwzPggeFcbbxh+M9jPEoqxDEMs62W6SsmC3BlyQqfARjJKqby+SkzpMHi6/c+R+z ULyf1pZsGb1Y+X1s19rXcKq04PXUfPSvHp/HHSnZxLJPJJfOl+IwVaQZikEEEsKoOBjaZWdI qOLGShLPcQSziuQywNby7TbQEEDnf0WqlwPcXA96hzvucsypC0ddB0nM7Gdax0FXPtHc3nM7 f6SmdRIybdHp9jFVsnL1OXqwD69OvkSp2c+xqeHqszJYBlSdBjx/UlfCPSP2emx+kh7ZQ0JD R3JlU0TS2+aU/GdFEiYJWhZynktkS5In6vcKf3MSRapzBUxepA/jZFX9sLkCbJJZSXMmuunf mxWxiYEqmLcOqK5pUrVdEXPX4I5kIPlPM5Z/6B9Zrwzh1DYhjVJWrmUtQ1Y4PdQR2KEadFWt o1kiYaGBTEgmkirQogGmMsjkU6wbbXAxc+ppAWBtGCdlESSV5XrEiFLdqmFzfQdW7x1946nD J9OwBDns9Vkk5yxU64AXfTBAh8mgNlaDQOrBpASkLr2MWUEMq71QOr3TXioU9Ie+acJVBtWX HYc2XJYKYVHiP9ENs3w9eA9zvUHOQOu10ZOJMt4ME6pyMHuFPHEnz5hjgzE6IAkcFoWEuJD4 N2jqoNUnIjfE01hqJN85gl5OqctTFLT9Y5+Ug4zoUgImU/orFzyts2sPWGqQZopy1NuDoUNg HTbqUkgV+XX1ITZCqz7+054sWamo5BfEZABXl2mOkztYMecWOVLDIsneGQY7B69xh65bEnF2 YkkF0OXuu7cebJuGyZFiFkQOrQcpc8X9X3zZrdpyUakMWJDsTm2rtp925zg7cVSoxuqKAXV7 uJqi/2nUqN1xGrUPWuPsTfyC7EaDsk38Xgkq4YsE7sJNuhySB3yOEylIQwmQ7hAnKYWswxby joP80sHK9I3XL2wka2tki58W/m6Qfcs63gX63gX6r42epx+sXaMP55sVv5deFh8W5ApupUeh FYH7OWpbU/mOL+UZOehSsKCzbPb5Lhgojqnrl1QVdupzRbsayrpDsTVbs+iFqXpsPjLSQRyp 9lkjDt6RtxXWm9QIFHa1q9k2ag0a+NHsGjjqpHOY0lDkcxCls/X5WVHD8fEKlJ1qRwuCht4e vSibyjrTXps+U4uX6sPvkODMQmdXy7qbIy7T7s2M/KlULRt2SJgGIhcEuFHk3k2MlG77hgxd MSXUP2dy5bTfly7FwukOTqSlbqaV/hY9+c4uXMtPbyhbFJ5xEpdafwwHIbeTUusyKEQUn8TF dB1WlGx0IFTl3rPvzmjNxJrPBu7F+6LThvsxQEL5dtiid2Rl2rYXXsIXsErXSFLMwJUkAObq kKU01hu7aFKRFlKseXQsZwKWsF2xBicn/OLHWh6su0XMXN+SVbN01uZaZ4o6zg7e1v+CITPj IvQw8YDk9oHJoqU46qBiN5xbW+LF2wWTReaUUTHenDy/6EkuLousDzhfLmHXq/l/M0/yW1oZ n0nL39I8vsQ4o4cYavtLxfrgVhdY96Y2S63qmaSc71+LXdWQZhbpWDkjpdOoaW2GsnP1eVC7 OLk5qYcoa9ZJ95ydPg+z5iuCRjLp1UKgVBCU60QpiWp9uHxyFWwnipNI+ifzgky9Aam1bCBH F9aPLyutd5nkIWhnDaWc9ZzdfMq+zTMqUnTN5dYy0uMAaMszWQbnyQMIYC6iDpaVMTajoPjz LLALRYvzn3hPyVGiePCs5jIEVUtGD2a5ydcI++KArcKfG6zl7+AS9lQApCCLQKkwpdevYaZb LJvd5NWygFwg5Ib0JvBBfxP2mFs3CDEn3GiyF8FZ9GgP/Crkg3X2db5H5FRtd99q+bzfocJr PNu7j80f0ReiMCiptvPnNDAT/ALAl/aeRKfLLHHAZrHS7j7RfTbLPStb4D+V9kT5Pe83wh0v RSBXSFfw7d5frRLqOL1TfOE6m3e9yt729TjLF8eIxtm6g7qk7StG9d0DQ1NRQwWtVqrOp6tE 81fU6oTsVvn2qPiWprOp69sjdKxueriU99D8qt21LWMEO8E/fA6ShVL= }
 
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