Polar Traps Tutorial for UltraFractal - Page 3

 

The Traps

Unlike Simple Traps Enhanced, where the various trap types and distance variants have distinct shapes, Polar Traps Enhanced shows more subtle differences among the trap types. This page of the tutorial will present some of the more distinctive trap types and an exploration of images created using trap variants = 4. This particular variant creates loops and ribbons which can vary appreciably among the trap types.

Cycloid Tschirnhausen Cubic
Lemniscate Lemniscate Loops
Rose Loops Trifolium Loops
PolarCycloid {
; Copyright  2007 by Ronald Barnett.
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}
PolarTschirn {
; Copyright  2007 by Ronald Barnett.
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}
PolarLemniscate {
; Copyright  2007 by Ronald Barnett.
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}
PolarLemniscateLoops {
; Copyright  2007 by Ronald Barnett.
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}
PolarRoseLoops {
; Copyright  2007 by Ronald Barnett.
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  77+dd29ObzIivrCTHwH3DstHT8S4xdKcwNwtaI32GYGOaiHzWhSRjNEPam4MVv1vp9GewKcS
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  aqu0djBrQXdg1cBXwVkd2xuDOeBY7/CSL925b2QVbHnbdpYXJ7gN3u+TMeVfSBUp5ir1mpnT
  Hgqt8Xw9I5WeRvt2J2UXXOxQFYz1yQR1WVv5iKeNsaxmdGa54GGtMecr04C+O2wokwX6tICg
  CtrswwKBtraRPSYLdIWEeIWksHWkOgF6QNcSoGOua0Rb4kFayE7Untd2NgZHjWZc/KCcHv1F
  2m1oCQqxA32eoreAtH70AWOpKLaarQz0hYMHqyirjdxCfT9SDQY8LMp5L46UsO3R7O92j96K
  L65gu4BorP1QtFFsH8hQj4XHAgDXKCAYfqCYXM9QKtEcyIAimcuGuPLRfvTRh7j76D96bD7Y
  /GcIo/7JQCOQ8yaG6MlrBXZ6s2CPYFOYFZRD9CfX3koYHfSBkar+ORbBMUYspQoEVydfQfFr
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  K7mowt+g0F3SagQPOO+WkCguBpAl0uXZiv5VCA5XSDeAs3/vCVBzFrqYTVEIAwkWNVDQ2oXu
  CZAfoGA3H/PrMgLpBYclcOZAnTDg1DfoMgrUDg9qlPWGw50AMK15DkBcBNADskPSGwtpBYPW
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  9ZlBcRNAudzzJD4iaAmww/jlBcZNADU8PjMgLqBonm/HJD4q0AMlk/plBcJNAT9wJlBcRNAD
  skPWGwNpBYkt9gMgbXDwBs+H5sfLaAGZHGPVXxtoBYKX39wirTDwAX/jlBcNaAmO7nQGwVpB
  4IO/T5zf9aA2zN9I4NqBYUBV8ho3VoBo/rynQGwtoBYgw/eyAueNA93fdgMgrUDQvahTLD4P
  DNAo4nHJvDFck0D6ptPUDKJNN1Q68rCt9wLQb//Lfs+wA0zZPnll9Vlf+PVBU+Okiu9ApGR5
  qNlM/jZrfwj2n9H/R7dc/v/s93f2+7Pb/9nt/+z2f/Z7v/s93f2+7Pb/pps/po0pU2DPggur
  BoX9c5/POl9cgJ2Kz3C2j1+JZpr33/G4tzjOiieHrlR18p/znb+Pvt1T/Lr5PGr8gZoso0sT
  yN/r9vnmZxh4kzQP3N/X8F1/fV65x3pnfne+d653pnfne+d653pn/NJ9ccQwI/8+f1LpPHjx
  hpH+7qBFEjeOJLe8HWz4PFHgQfCCG3R/yaQxpZpRRZH/TrJKMNLCFeTE+/3A3vZviB==
}
PolarTrifoliumLoop {
; Copyright  2006 by Ronald Barnett.
; Tweakable
::MSoDRjn2tvVSPuuNS47NQ/fQQnyy0uFpWsVC4BrsAMBJADSydDaJZbhn2iEdvYkf8TxNJa1t
  3GgGvHmQfqKuUsqiFp++Mk20RTZ0yv7+7ccYFsyci7/ppk29ndFbaKL2X9rNNtuOPXkx2RiC
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  793JMkwFqyZ7ayIV7LZFt0+enUaLropm4+r8x4gQuONt00C2rEknnDrjW33S7yrZkXz7lmob
  beVTWOpvZDrk7t3fXFtttoerYNShBn3RewbWEK2fu3cUQc4jezwxxIvwFe4YnK62aCeWQg3i
  FBxO06tQi5BUQws4Qc493tppDcRq0lpvUwtH4OeOt5dp7yT/EpZzGnNFl510KIl2lve2+NVu
  OwS39Kx9X2XWQToFlN7Zucj0uil3zIgbDirldIsIYyVtIuzO3PEHEA+ZIGJcii6+isc5OHPN
  sBci6m687vDm8b7qsoOn250D7qZkFBehehRTdx0Sh3o8SRhAM/2+V/U9OadaemL4OPBb68tE
  0sQQL/FImZwCrCDY4rEZ/fGm7OIogGTbKb6kt+vhUFlvjKHeWRPUfwg1XL5IGcPfhgJIUI+K
  D/EtjEI7gg4GYzqN1+k0meoRZJq3ME3r6hKMYCi8haygMfq0+PprUaX1JUFdsmmK6Q6UM2rt
  gTtcdvDrBOfwdnMxyqsW9+KpL0uiWWKKAkTu/TFtE+uWdzqmNr490L05Sbpy+apMQrm4Nm0W
  +s8g1SleiSPRpLKrJuVF1f1y/VyX7KD/qN7rTXSgN7amWNhQZ0aRaql4+NumGguufYriHmSr
  K98NrULiIfwTALJM91A84cJkdx8U1SYvX56wRDezeiIP/5BZGs7LUeU2AceA2TMbpq5JYB0O
  DXjWBDA9onYt6Z5yc16RxuG2oiY5kaSTIXTZLCjISrm6QIlQWCnQLqyzExM4+cXSFLJ6AMhH
  gyuTMiuEzoLRHLyJLDwkJBYiqqTGdJ6oLZM6SMDBIATOKAN0Er5kobQXOdVJjc5newH2gXXp
  6rW6tKLV3nSh73GCFYcbgLfkWRNyHQP+go2/41ongVSpkQ98bfuTn/yy4LqsgiLxbmfoFR6/
  rOhEmQ5nf5iRkum91ZqdzdNPrn5OKWKlC3CBFocHpScdi7hv9vP838S8Dy+QEXeDqiK+Ywvd
  QY5g0jw/tjw30MwVcI1OHI6PKiHFDGFDHFj4iqz4Pr33eGPI5PIFMIFOIFpkgjxfr84e9e+B
  8hj7SV8Ed/J6BSdTLESOk31MoGJV57XPxU3GweBKYFPjV0c241G5p8e8kirKqLYkD8MHc8CS
  s/JUW6cwVshyeJYwX4ahjeicyibZ/h8iSxAgWEXdtTs8F0h80LFr1paQOFPmV5GRW9iM1waV
  2LsheKLqAXFL2ZoZBjGhrq30Emo4gh9AkAyMCkFa3KrD3WT7KXJSDSTIb4och/0cR0R5i5m5
  Ce06bEt+GR7Y9GNLyQe+YAIXdRysLnKTmbJwd9D9xzKA+nxctoZZ220Gj5SDdsRDckPEh4QT
  y8K6IzozgS1GAi5T59kQVJWn6cdHf7ReXlM1JtBP7FON7h8OK9hQKV+khs34lgc1168HInak
  zAjYoYcoGuPLifpTaqOQYd8D98bD7y/L4cgsJokc2cpovSsfHYKxI5SY985K+DNDVbCH/QnR
  UcowQBxehfnITDrBD6j96Da0+C+T13m3oS5eKNeJK/052OaWBMDJK3mqKQGwd/HFVtl5OQvv
  K2Od0jbmrTfVTDgaiXgDP7RAMjfmnbgC484LwaIhgFvIOexcVjIffVzL8Dj88Qq2xRRq29DW
  E7tADQRlg1Fukaxg9ett1Q5xhh3ELAvbgFA8o3Ow0/TmDAUG1LyVAi9hhR7S5wE/MzHQeKnf
  rlrJdgaI5SL1QDV0AW8e0AOBHA1hwLRD495AMiP+qoBcCOASrcV0AmyBYM3dJaAnlDgO/dCa
  AnnDgyHuENgTwBwES+VRDYCHAFi8biGwb4AYwu6qoB8WOADkcuMNgzyB4ISOnhGwZ4AYkRPJ
  NgLwBYAe/FoBcOOAa0snjGwF5AofI35oBcJOAGQ8PJNgLzBwwKnmGwF5AMwT4M0AOLHAdW9S
  0AuAHATM+ngGw55Aoq3PLNgTxBYE821RDYKHAdRxNRD4YOATIFct0AM5AYYibhGwEOAj5irj
  Gwp4AMQP480AOHHgpw7PFNgpcAeDtgrjGwEOAmW5qpB8GOA6SjriGwp4AMS27qoB8OcAGYGc
  N0AePOA644y0AODHAVK9jmGwD4wRaAo5hKk9oo5znDoPVdAjS1BeRMA6/jCyf8Ng4XakSLk/
  vMh8/bQWugtPL3C43C43C43C43C43C43C43C43C4/zKgfEyAvPShq3T/X7P0imAwH1/tvv9/
  2//TA6/78rlsY8tY8tY8tY8tY8tY8tY8tY8tY8/s+n6j89HR5HN/E/p+jvgPefUw8xXAmvFR
  f0Xa45/RAXJ3SWM9WM9WM9WM9WM9WM9WM9WM9WM9fmfRdevXY/38e6459BDpfxRI6tfztQXi
  CEJq9A8iow4Qk/HKwd3/AQjXyRuzbz99eX7r0v+NuT+EclQ5vBc8qP6wb67u1AHvc6/v8d3e
  MOeFerb67u1ij3ij3ij3ij3ij3ij3ij3ij/LYc8hxY0i4FqmDHaHBwiBY06XYH5c1zJMGF5H
  r7bcSBwasYh2YjcCiij8QhRjLPeYO+eY/xp47N6AB+R8vLAVHhH5AewyjjvJmG/X6wSybB==
}
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