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&#039;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&#039;ve also added four new dynamical systems functions to mt.ulb. Three are examples from Pickover&#039;s book _Computers, Pattern, Chaos and Beauty_. The other, called &quot;Alternate&quot;, lets you load two functions and use them on alternate iterations.

0

Here's a quick test run of this formula. This uses the CPCB Figure 14.14 plug-in.

`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=}`

Here&#039;s a quick test run of this formula. This uses the CPCB Figure 14.14 plug-in. ![5bd0b6d5a2fa5.jpg](serve/attachment&amp;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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