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Fractales   unidimensionales

Cantor=List[
    List[{{.33,   0.},{0.,     .33}},{   0., .4}],
    List[{{.33,   0.},{0.,     .33}},{   .67, .4}]
];

CantorTwoScales=List[
   List[{{0.5,   0}, {0,0.5}},      {0,     0}],
   List[{{0.2,   0}, {0,0.2}},      {0.8,   0}]
];

Fractales   bidimensionales




Koch=List[
     List[{{ 0.333, 0.0},{0.0,0.333}},{0.0,      0.0 }],
     List[{{0.167,  -0.288},{0.288,0.167}},{0.333,     0.0   }],
     List[{{0.167,  0.288},{-0.288,0.167}},{0.5,     0.288   }],
     List[{{.333,  0.},{0.,.333}},{.667,    0.}]
];




Koch2=List[
       List[{{0.31,0.00},{0.00,0.29}},{4.12,1.60}],
       List[{{0.19,-0.21},{0.65,0.09}},{-0.69,5.98}],
     List[{{0.19,0.21},{-0.65,0.09}},{0.67,5.96}],
     List[{{0.31,0.00},{0.00,0.29}},{-4.14,1.60}],
     List[{{0.38,0.00},{0.00,-0.29}},{-0.01,2.94}]
];
(* Barnsley's   Fern *)
Fern=List[
     List[{{0.81,0.07},{-0.04,0.84}},{0.12,0.195}],
     List[{{0.18,-0.25},{0.27,0.23}},{0.12,0.02}],
     List[{{0.19,0.275},{0.238,-0.14}},{0.16,0.12}],
     List[{{0.0235,0.087},{0.045,0.1666}},{0.11,0.0}]
];




Sierpinsky=List[
     List[{{0.5,0.},{0.,0.5}},{-1.,1.}],
     List[{{0.5,0.},{0.,0.5}},{1.,    1.}],
     List[{{0.5,0.},{0.,0.5}},{0.,-1.}]
];




Coral=List[
              List[{{0.31,-0.53},{-0.46,-0.29}},{      5.40,8.66}],
              List[{{0.31,-0.08},{    0.15,-0.45}},{-1.30,4.15}],
List[{{0.00,     0.55},{   0.69,-0.20}},{-4.89,7.27}]
];

Twig=List[
                List[{{-0.46,0.02},{-0.11,0.01}},{0.4,0.4}],
                List[{{0.39,0.43},{0.43,-0.39}},{0.26,0.52}],
                List[{{0.44,-0.09},{-0.01,-0.32}},{0.42,0.51}]
];




Crystal=List[
                 List[{{0.255,     0.},{0.,   0.255}},{0.372,    0.671}],
                 List[{{0.255,     0.},{0.,   0.255}},{0.115,    0.223}],
                 List[{{0.255,     0.},{0.,   0.255}},{0.631,    0.223}],
                 List[{{0.37,     -0.642},{0.642,    0.37}},{0.636,    -0.006}]
];

Tree1=List[
     List[{{ 0.05 ,     0} , { 0 ,.5 }},{         0 , 0}],
     List[{{.42 ,-.42},   {.42 , .42 }},{        0, .2 }],
     List[{{.42 , .42} ,{-.42 ,.42 }},{          0, .2 }]
];




Tree=List[
     List[{{0.195,    -0.448},{0.334,      0.443}},    {0.443,   0.245}],
List[{{0.462   ,0.414},{-0.252,   0.361}},     {0.251, 0.569}],
     List[{{-0.058,-0.07},{0.453,-0.111}},                  {0.598, 0.097}],
     List[{{-0.035,   0.07},{-0.469,   -0.022}},    {0.488,   0.507}],
     List[{{-0.637,   0.},    {0., 0.501}},
       {0.856, 0.251}]
];




ChristmasTree=List[
               List[{{0.,  -0.5},{0.5,   0.}},{0.5,    0.}],
               List[{{0.,  0.5},{-0.5,   0.}},{0.5,    0.5}],
               List[{{0.5,  0.},{0.,   0.5}},{0.25,    0.5}]
];

Leaf=List[
      List[{{0.515152,-0.719697},{-0.636364,-0.397727}},
            {4.301069,6.186183}],
      List[{{-0.515152,0.219697},{-0.242424,-0.234848}},
            {-3.667063,8.847470}]
];




Spiral=List[
               List[{{0.79,-0.42},{0.24,0.86}},{1.76,1.41}],
                List[{{-0.12,0.26},{0.15,0.05}},{-6.72,1.38}],
                List[{{0.18,-0.14},{0.09,0.18}},{6.09,1.57}]
];

ZigZag=List[
               List[{{-0.63,-0.61},{-0.55,0.66}},{3.84,1.28}],
                 List[{{-0.04,0.44},{0.21,0.04}},{2.07,8.33}]
];
Dragon=List[
               List[{{0.82,0.28},{-0.21,0.86}},{-1.88,-0.11}],
               List[{{0.09,0.52},{-0.46,-0.38}},{0.79,8.10}]
];




Bones=List[
             List[{{ 0.771,-0.485},{-0.419,-0.725}},{     2.094,7.425}],
      List[{{-0.259,-0.109},{-0.136,    0.171}},{   5.865,0.737}],
      List[{{ 0.309, 0.125},{    0.265,-0.074}},{-5.623,8.169}]
];




Noisy=List[
      List[{{0.424,-0.651},{-0.485,-0.345}},{      3.964,        4.222}],
      List[{{-0.080,-0.203},{-0.743,     0.205}},{-4.092,         3.957}]
];
Neuron=List[
               List[{{0.636,-0.727},{-0.636,-0.398}},{      3.433,6.078}],
               List[{{0.030,-0.189},{    0.666,-0.167}},{    0.527,3.675}],
               List[{{0.212,   0.049},{   0.273, 0.545}},{   3.038,1.347}],
               List[{{0.090,   0.182},{-0.152,   0.447}},{-3.220,5.596}]
];




Gather=List[
               List[{{-0.312,-0.832},{    0.812,-0.283}},{    3.870,7.404}],
               List[{{0.125,   0.317},{-0.187,-0.130}},{     2.043,7.917}],
               List[{{-0.062,-0.197},{    0.250,   0.173}},{-3.132,0.846}]
];

Cloud=List[
                     List[{{ 0.75,0.},{0.,-0.75}},{    1.025,8.419}],
                     List[{{-0.75,0.},{0.,   0.75}},{-1.468,1.203}],
                     List[{{-0.75,0.},{0.,   0.75}},{-2.549,2.283}],
                     List[{{ 0.75,0.},{0.,-0.75}},{    2.106,7.338}]
];
Blocks=List[
     List[{{ 0.0,0.3},{0.54,0.}},{.69,.44}],
     List[{{-0.65,0.},{0.,   .41}},{.66,.57}],
     List[{{ 0.24,0.},{0.,-.32}},{.33,.35}],
     List[{{ 0.38,0.},{0.,    .41}},{.6,.02}],
     List[{{-0.28,0.},{0.,-.523}},{.3,.53}]
];




Abestos=List[
             List[{{ 0.308,-0.531},{-0.461,-0.294}},{     4.123,7.711}],
             List[{{ 0.308,-0.077},{   0.153,-0.448}},{-1.536,5.002}],
             List[{{ 0.000, 0.545},{   0.692,-0.196}},{-5.296,7.590}],
             List[{{-0.308,-0.014},{   0.231,-0.399}},{   2.393,5.071}]
];




Leaf2=List[
              List[{{   0.242,-0.640},{-0.909,-0.318}},{   4.612,5.593}],
List[{{-0.091,-0.557},{-0.485,     0.155}},{-1.064,5.654}]
];




Art=List[
            List[{{ 0.75,-0.46},{    0.41, 0.89}},{1.46,0.69}],
            List[{{-0.42,-0.07},{-0.18,-0.22}},{3.81,6.74}]
];




Chaos=List[
      List[{{0, 0.053},{-0.429,    0}},{-7.083,    5.43}],
      List[{{0.143,   0},{0, -0.053}},{-5.619,     8.513}],
      List[{{0.143,   0},{0, 0.083}},{-5.619,     2.057 }],
      List[{{0, 0.053},{0.429,    0}},{-3.952,    5.43 }],
      List[{{0.119,   0},{0, 0.053}},{-2.555,     4.536 }],
      List[{{-0.0123806,-0.0649723},{0.423819,0.00189797}},{-1.226,
5.235}],
      List[{{0.0852291,0.0506328},{0.420449,0.0156626}},{-0.421,
4.569}],
      List[{{0.104432,0.00529117},{0.0570516,0.0527352}},{0.976,
8.113}],
      List[{{-0.00814186,-0.0417935},{0.423922,0.00415972}},{1.934,
5.37}],
      List[{{0.093,   0},{0, 0.053}},{0.861,     4.536 }],
      List[{{0, 0.053},{-0.429,    0}},{2.447,    5.43 }],
      List[{{0.119,   0},{0, -0.053}},{3.363,     8.513 }],
      List[{{0.119,   0},{0, 0.053}},{3.363,     1.487 }],
      List[{{0, 0.053},{0.429,    0}},{3.972,    4.569 }],
      List[{{0.123998,   -0.00183957},{0.000691208,     0.0629731}},{6.275,
7.716}],
      List[{{0, 0.053},{0.167,    0}},{5.215,    6.483 }],
      List[{{0.071,   0},{0, 0.053}},{6.279,     5.298 }],
      List[{{0, -0.053},{-0.238,     0}},{6.805,   3.714 }],
      List[{{-0.121,   0},{0, 0.053}},{5.941,     1.487 }]
];

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Codigos Ifs

  • 1. Fractales unidimensionales Cantor=List[ List[{{.33, 0.},{0., .33}},{ 0., .4}], List[{{.33, 0.},{0., .33}},{ .67, .4}] ]; CantorTwoScales=List[ List[{{0.5, 0}, {0,0.5}}, {0, 0}], List[{{0.2, 0}, {0,0.2}}, {0.8, 0}] ]; Fractales bidimensionales Koch=List[ List[{{ 0.333, 0.0},{0.0,0.333}},{0.0, 0.0 }], List[{{0.167, -0.288},{0.288,0.167}},{0.333, 0.0 }], List[{{0.167, 0.288},{-0.288,0.167}},{0.5, 0.288 }], List[{{.333, 0.},{0.,.333}},{.667, 0.}] ]; Koch2=List[ List[{{0.31,0.00},{0.00,0.29}},{4.12,1.60}], List[{{0.19,-0.21},{0.65,0.09}},{-0.69,5.98}], List[{{0.19,0.21},{-0.65,0.09}},{0.67,5.96}], List[{{0.31,0.00},{0.00,0.29}},{-4.14,1.60}], List[{{0.38,0.00},{0.00,-0.29}},{-0.01,2.94}] ];
  • 2. (* Barnsley's Fern *) Fern=List[ List[{{0.81,0.07},{-0.04,0.84}},{0.12,0.195}], List[{{0.18,-0.25},{0.27,0.23}},{0.12,0.02}], List[{{0.19,0.275},{0.238,-0.14}},{0.16,0.12}], List[{{0.0235,0.087},{0.045,0.1666}},{0.11,0.0}] ]; Sierpinsky=List[ List[{{0.5,0.},{0.,0.5}},{-1.,1.}], List[{{0.5,0.},{0.,0.5}},{1., 1.}], List[{{0.5,0.},{0.,0.5}},{0.,-1.}] ]; Coral=List[ List[{{0.31,-0.53},{-0.46,-0.29}},{ 5.40,8.66}], List[{{0.31,-0.08},{ 0.15,-0.45}},{-1.30,4.15}],
  • 3. List[{{0.00, 0.55},{ 0.69,-0.20}},{-4.89,7.27}] ]; Twig=List[ List[{{-0.46,0.02},{-0.11,0.01}},{0.4,0.4}], List[{{0.39,0.43},{0.43,-0.39}},{0.26,0.52}], List[{{0.44,-0.09},{-0.01,-0.32}},{0.42,0.51}] ]; Crystal=List[ List[{{0.255, 0.},{0., 0.255}},{0.372, 0.671}], List[{{0.255, 0.},{0., 0.255}},{0.115, 0.223}], List[{{0.255, 0.},{0., 0.255}},{0.631, 0.223}], List[{{0.37, -0.642},{0.642, 0.37}},{0.636, -0.006}] ]; Tree1=List[ List[{{ 0.05 , 0} , { 0 ,.5 }},{ 0 , 0}], List[{{.42 ,-.42}, {.42 , .42 }},{ 0, .2 }], List[{{.42 , .42} ,{-.42 ,.42 }},{ 0, .2 }] ]; Tree=List[ List[{{0.195, -0.448},{0.334, 0.443}}, {0.443, 0.245}],
  • 4. List[{{0.462 ,0.414},{-0.252, 0.361}}, {0.251, 0.569}], List[{{-0.058,-0.07},{0.453,-0.111}}, {0.598, 0.097}], List[{{-0.035, 0.07},{-0.469, -0.022}}, {0.488, 0.507}], List[{{-0.637, 0.}, {0., 0.501}}, {0.856, 0.251}] ]; ChristmasTree=List[ List[{{0., -0.5},{0.5, 0.}},{0.5, 0.}], List[{{0., 0.5},{-0.5, 0.}},{0.5, 0.5}], List[{{0.5, 0.},{0., 0.5}},{0.25, 0.5}] ]; Leaf=List[ List[{{0.515152,-0.719697},{-0.636364,-0.397727}}, {4.301069,6.186183}], List[{{-0.515152,0.219697},{-0.242424,-0.234848}}, {-3.667063,8.847470}] ]; Spiral=List[ List[{{0.79,-0.42},{0.24,0.86}},{1.76,1.41}], List[{{-0.12,0.26},{0.15,0.05}},{-6.72,1.38}], List[{{0.18,-0.14},{0.09,0.18}},{6.09,1.57}] ]; ZigZag=List[ List[{{-0.63,-0.61},{-0.55,0.66}},{3.84,1.28}], List[{{-0.04,0.44},{0.21,0.04}},{2.07,8.33}] ];
  • 5. Dragon=List[ List[{{0.82,0.28},{-0.21,0.86}},{-1.88,-0.11}], List[{{0.09,0.52},{-0.46,-0.38}},{0.79,8.10}] ]; Bones=List[ List[{{ 0.771,-0.485},{-0.419,-0.725}},{ 2.094,7.425}], List[{{-0.259,-0.109},{-0.136, 0.171}},{ 5.865,0.737}], List[{{ 0.309, 0.125},{ 0.265,-0.074}},{-5.623,8.169}] ]; Noisy=List[ List[{{0.424,-0.651},{-0.485,-0.345}},{ 3.964, 4.222}], List[{{-0.080,-0.203},{-0.743, 0.205}},{-4.092, 3.957}] ];
  • 6. Neuron=List[ List[{{0.636,-0.727},{-0.636,-0.398}},{ 3.433,6.078}], List[{{0.030,-0.189},{ 0.666,-0.167}},{ 0.527,3.675}], List[{{0.212, 0.049},{ 0.273, 0.545}},{ 3.038,1.347}], List[{{0.090, 0.182},{-0.152, 0.447}},{-3.220,5.596}] ]; Gather=List[ List[{{-0.312,-0.832},{ 0.812,-0.283}},{ 3.870,7.404}], List[{{0.125, 0.317},{-0.187,-0.130}},{ 2.043,7.917}], List[{{-0.062,-0.197},{ 0.250, 0.173}},{-3.132,0.846}] ]; Cloud=List[ List[{{ 0.75,0.},{0.,-0.75}},{ 1.025,8.419}], List[{{-0.75,0.},{0., 0.75}},{-1.468,1.203}], List[{{-0.75,0.},{0., 0.75}},{-2.549,2.283}], List[{{ 0.75,0.},{0.,-0.75}},{ 2.106,7.338}] ];
  • 7. Blocks=List[ List[{{ 0.0,0.3},{0.54,0.}},{.69,.44}], List[{{-0.65,0.},{0., .41}},{.66,.57}], List[{{ 0.24,0.},{0.,-.32}},{.33,.35}], List[{{ 0.38,0.},{0., .41}},{.6,.02}], List[{{-0.28,0.},{0.,-.523}},{.3,.53}] ]; Abestos=List[ List[{{ 0.308,-0.531},{-0.461,-0.294}},{ 4.123,7.711}], List[{{ 0.308,-0.077},{ 0.153,-0.448}},{-1.536,5.002}], List[{{ 0.000, 0.545},{ 0.692,-0.196}},{-5.296,7.590}], List[{{-0.308,-0.014},{ 0.231,-0.399}},{ 2.393,5.071}] ]; Leaf2=List[ List[{{ 0.242,-0.640},{-0.909,-0.318}},{ 4.612,5.593}],
  • 8. List[{{-0.091,-0.557},{-0.485, 0.155}},{-1.064,5.654}] ]; Art=List[ List[{{ 0.75,-0.46},{ 0.41, 0.89}},{1.46,0.69}], List[{{-0.42,-0.07},{-0.18,-0.22}},{3.81,6.74}] ]; Chaos=List[ List[{{0, 0.053},{-0.429, 0}},{-7.083, 5.43}], List[{{0.143, 0},{0, -0.053}},{-5.619, 8.513}], List[{{0.143, 0},{0, 0.083}},{-5.619, 2.057 }], List[{{0, 0.053},{0.429, 0}},{-3.952, 5.43 }], List[{{0.119, 0},{0, 0.053}},{-2.555, 4.536 }], List[{{-0.0123806,-0.0649723},{0.423819,0.00189797}},{-1.226, 5.235}], List[{{0.0852291,0.0506328},{0.420449,0.0156626}},{-0.421, 4.569}], List[{{0.104432,0.00529117},{0.0570516,0.0527352}},{0.976, 8.113}], List[{{-0.00814186,-0.0417935},{0.423922,0.00415972}},{1.934, 5.37}], List[{{0.093, 0},{0, 0.053}},{0.861, 4.536 }], List[{{0, 0.053},{-0.429, 0}},{2.447, 5.43 }], List[{{0.119, 0},{0, -0.053}},{3.363, 8.513 }], List[{{0.119, 0},{0, 0.053}},{3.363, 1.487 }], List[{{0, 0.053},{0.429, 0}},{3.972, 4.569 }], List[{{0.123998, -0.00183957},{0.000691208, 0.0629731}},{6.275, 7.716}], List[{{0, 0.053},{0.167, 0}},{5.215, 6.483 }], List[{{0.071, 0},{0, 0.053}},{6.279, 5.298 }], List[{{0, -0.053},{-0.238, 0}},{6.805, 3.714 }], List[{{-0.121, 0},{0, 0.053}},{5.941, 1.487 }] ];