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Author Topic: A new 3d mandelbrot-like fractal  (Read 6667 times)
0 Members and 1 Guest are viewing this topic.
kram1032
Fractal Senior
******
Posts: 1863


« Reply #15 on: January 14, 2010, 08:16:46 PM »

in that case, the first pic looks better smiley
Logged
Tglad
Fractal Molossus
**
Posts: 703


WWW
« Reply #16 on: January 16, 2010, 04:32:40 AM »

Here's the code.
Use the basic vector class given earlier in this thread.
This defines the tetrahedron axes and the mapping lookup table:
Code:
  Vector corners[4]
  corners[0] = new Vector()
  corners[1] = new Vector()
  corners[2] = new Vector()
  corners[3] = new Vector()
  corners[0].Init(0, 1, 0)
  corners[1].Init(0, -1/3, sqrt(8/9))
  corners[2].Init(-sqrt(2/3), -1/3, -(1/3) * sqrt(2))
  corners[3].Init(sqrt(2/3), -1/3, -(1/3) * sqrt(2))
  Vector normals[4]
  Vector crosses[4*3]
  Vector C = new Vector()
  Vector temp1 = new Vector()
  Vector temp2 = new Vector()
  int triangles[4,3]
  triangles[0 , 0] = 0
  triangles[0 , 1] = 1
  triangles[0 , 2] = 2
  triangles[1 , 0] = 2
  triangles[1 , 1] = 3
  triangles[1 , 2] = 0
  triangles[2 , 0] = 1
  triangles[2 , 1] = 0
  triangles[2 , 2] = 3
  triangles[3 , 0] = 3
  triangles[3 , 1] = 2
  triangles[3 , 2] = 1
  Vector posit = new Vector()
  Vector bary = new Vector()
  int it = 0
  repeat
    normals[it] = new Vector()
    crosses[it*3 + 0] = new Vector()
    crosses[it*3 + 1] = new Vector()
    crosses[it*3 + 2] = new Vector()
    Vector cr1 = new Vector()
    cr1.Subtract(corners[triangles[it, 2]], corners[triangles[it, 0]])
    Vector cr2 = new Vector()
    cr2.Subtract(corners[triangles[it, 1]], corners[triangles[it, 0]])

    normals[it].Cross(cr1, cr2)
    normals[it].Normalise()
    crosses[it*3 + 0].Cross(corners[triangles[it, 2]], corners[triangles[it, 1]])
    crosses[it*3 + 1].Cross(corners[triangles[it, 0]], corners[triangles[it, 2]])
    crosses[it*3 + 2].Cross(corners[triangles[it, 1]], corners[triangles[it, 0]])
  until (it=it+1)>=4
  int maxI = 29
  int maxJ = 29
  Vector point[29, 29]
  it = 0
  repeat
    int it2 = 0
    repeat
      point[it, it2] = new Vector()
    until (it2=it2+1)>=maxJ
  until (it=it+1)>=maxI
point[0, 0].Init(-0.000000, 1.000000, -0.000000)
point[0, 1].Init(0.000000, 0.998399, 0.056569)
point[0, 2].Init(0.000000, 0.991307, 0.131572)
point[0, 3].Init(0.000000, 0.973080, 0.230469)
point[0, 4].Init(0.000000, 0.936487, 0.350702)
point[0, 5].Init(0.000000, 0.874871, 0.484356)
point[0, 6].Init(0.000000, 0.784014, 0.620742)
point[0, 7].Init(0.000000, 0.664315, 0.747452)
point[0, 8].Init(0.000000, 0.521831, 0.853049)
point[0, 9].Init(0.000000, 0.367160, 0.930158)
point[0, 10].Init(-0.000000, 0.211831, 0.977306)
point[0, 11].Init(-0.000000, 0.069162, 0.997605)
point[0, 12].Init(0.000000, -0.054627, 0.998507)
point[0, 13].Init(-0.000000, -0.154932, 0.987925)
point[0, 14].Init(0.000000, -0.221023, 0.975269)
point[0, 15].Init(-0.000000, -0.154932, 0.987925)
point[0, 16].Init(0.000000, -0.054627, 0.998507)
point[0, 17].Init(-0.000000, 0.069162, 0.997605)
point[0, 18].Init(-0.000000, 0.211831, 0.977306)
point[0, 19].Init(0.000000, 0.367160, 0.930158)
point[0, 20].Init(0.000000, 0.521831, 0.853049)
point[0, 21].Init(0.000000, 0.664315, 0.747452)
point[0, 22].Init(0.000000, 0.784014, 0.620742)
point[0, 23].Init(0.000000, 0.874871, 0.484356)
point[0, 24].Init(0.000000, 0.936487, 0.350702)
point[0, 25].Init(0.000000, 0.973080, 0.230469)
point[0, 26].Init(0.000000, 0.991307, 0.131572)
point[0, 27].Init(0.000000, 0.998399, 0.056569)
point[0, 28].Init(0.000000, 1.000000, -0.000000)
point[1, 0].Init(-0.048990, 0.998399, -0.028285)
point[1, 1].Init(-0.077757, 0.995961, 0.044893)
point[1, 2].Init(-0.101182, 0.985334, 0.137398)
point[1, 3].Init(-0.121577, 0.960448, 0.250516)
point[1, 4].Init(-0.139000, 0.914261, 0.380533)
point[1, 5].Init(-0.152516, 0.840842, 0.519349)
point[1, 6].Init(-0.160861, 0.737644, 0.655747)
point[1, 7].Init(-0.162931, 0.607311, 0.777577)
point[1, 8].Init(-0.158176, 0.457943, 0.874796)
point[1, 9].Init(-0.146728, 0.301378, 0.942148)
point[1, 10].Init(-0.128930, 0.149402, 0.980335)
point[1, 11].Init(-0.106630, 0.010238, 0.994246)
point[1, 12].Init(-0.082096, -0.111885, 0.990324)
point[1, 13].Init(-0.066067, -0.220480, 0.973151)
point[1, 14].Init(0.048105, -0.229677, 0.972077)
point[1, 15].Init(0.081081, -0.115864, 0.989950)
point[1, 16].Init(0.106321, 0.009009, 0.994291)
point[1, 17].Init(0.128888, 0.148895, 0.980417)
point[1, 18].Init(0.146778, 0.301067, 0.942239)
point[1, 19].Init(0.158272, 0.457703, 0.874905)
point[1, 20].Init(0.163071, 0.607129, 0.777690)
point[1, 21].Init(0.161030, 0.737515, 0.655851)
point[1, 22].Init(0.152693, 0.840759, 0.519431)
point[1, 23].Init(0.139166, 0.914213, 0.380589)
point[1, 24].Init(0.121719, 0.960423, 0.250546)
point[1, 25].Init(0.101292, 0.985322, 0.137405)
point[1, 26].Init(0.077824, 0.995956, 0.044883)
point[1, 27].Init(0.049018, 0.998397, -0.028300)
point[2, 0].Init(-0.113945, 0.991307, -0.065786)
point[2, 1].Init(-0.169581, 0.985334, 0.018928)
point[2, 2].Init(-0.216753, 0.968172, 0.125143)
point[2, 3].Init(-0.257142, 0.933392, 0.250315)
point[2, 4].Init(-0.290242, 0.874377, 0.388876)
point[2, 5].Init(-0.314221, 0.786440, 0.531768)
point[2, 6].Init(-0.326869, 0.668951, 0.667579)
point[2, 7].Init(-0.326477, 0.526592, 0.784929)
point[2, 8].Init(-0.312500, 0.368931, 0.875348)
point[2, 9].Init(-0.284659, 0.207071, 0.935997)
point[2, 10].Init(-0.243821, 0.051782, 0.968437)
point[2, 11].Init(-0.191975, -0.091384, 0.977136)
point[2, 12].Init(-0.128816, -0.221749, 0.966558)
point[2, 13].Init(-0.001597, -0.288439, 0.957497)
point[2, 14].Init(0.124471, -0.220867, 0.967329)
point[2, 15].Init(0.191008, -0.092266, 0.977243)
point[2, 16].Init(0.243511, 0.051053, 0.968554)
point[2, 17].Init(0.284651, 0.206488, 0.936129)
point[2, 18].Init(0.312633, 0.368441, 0.875507)
point[2, 19].Init(0.326696, 0.526189, 0.785108)
point[2, 20].Init(0.327156, 0.668643, 0.667746)
point[2, 21].Init(0.314537, 0.786221, 0.531905)
point[2, 22].Init(0.290551, 0.874232, 0.388972)
point[2, 23].Init(0.257415, 0.933302, 0.250368)
point[2, 24].Init(0.216974, 0.968121, 0.125154)
point[2, 25].Init(0.169738, 0.985308, 0.018903)
point[2, 26].Init(0.114030, 0.991294, -0.065835)
point[3, 0].Init(-0.199591, 0.973080, -0.115234)
point[3, 1].Init(-0.277741, 0.960448, -0.019968)
point[3, 2].Init(-0.345350, 0.933392, 0.097534)
point[3, 3].Init(-0.402506, 0.885430, 0.232387)
point[3, 4].Init(-0.447531, 0.810735, 0.377392)
point[3, 5].Init(-0.477655, 0.706116, 0.522729)
point[3, 6].Init(-0.489974, 0.572725, 0.657199)
point[3, 7].Init(-0.482391, 0.416697, 0.770495)
point[3, 8].Init(-0.453515, 0.247765, 0.856117)
point[3, 9].Init(-0.402304, 0.076831, 0.912277)
point[3, 10].Init(-0.328549, -0.085346, 0.940623)
point[3, 11].Init(-0.230617, -0.231357, 0.945140)
point[3, 12].Init(-0.088550, -0.334680, 0.938162)
point[3, 13].Init(0.087116, -0.334182, 0.938474)
point[3, 14].Init(0.229077, -0.231382, 0.945509)
point[3, 15].Init(0.328016, -0.085969, 0.940752)
point[3, 16].Init(0.402177, 0.076119, 0.912392)
point[3, 17].Init(0.453616, 0.247069, 0.856265)
point[3, 18].Init(0.482611, 0.416056, 0.770704)
point[3, 19].Init(0.490318, 0.572216, 0.657386)
point[3, 20].Init(0.478058, 0.705730, 0.522882)
point[3, 21].Init(0.447940, 0.810459, 0.377498)
point[3, 22].Init(0.402881, 0.885244, 0.232444)
point[3, 23].Init(0.345663, 0.933275, 0.097542)
point[3, 24].Init(0.277975, 0.960380, -0.020008)
point[3, 25].Init(0.199737, 0.973040, -0.115318)
point[4, 0].Init(-0.303716, 0.936487, -0.175351)
point[4, 1].Init(-0.399051, 0.914262, -0.069889)
point[4, 2].Init(-0.481897, 0.874377, 0.056920)
point[4, 3].Init(-0.550596, 0.810735, 0.198878)
point[4, 4].Init(-0.602318, 0.718530, 0.347748)
point[4, 5].Init(-0.633502, 0.595954, 0.493471)
point[4, 6].Init(-0.640569, 0.445452, 0.625495)
point[4, 7].Init(-0.620500, 0.273958, 0.734798)
point[4, 8].Init(-0.569830, 0.091241, 0.816682)
point[4, 9].Init(-0.485719, -0.090167, 0.869452)
point[4, 10].Init(-0.365861, -0.256071, 0.894748)
point[4, 11].Init(-0.203237, -0.385654, 0.899981)
point[4, 12].Init(-0.000300, -0.437949, 0.899000)
point[4, 13].Init(0.202491, -0.385591, 0.900176)
point[4, 14].Init(0.365252, -0.256439, 0.894891)
point[4, 15].Init(0.485484, -0.090864, 0.869511)
point[4, 16].Init(0.569854, 0.090435, 0.816755)
point[4, 17].Init(0.620699, 0.273168, 0.734923)
point[4, 18].Init(0.640900, 0.444764, 0.625645)
point[4, 19].Init(0.633928, 0.595400, 0.493594)
point[4, 20].Init(0.602771, 0.718110, 0.347830)
point[4, 21].Init(0.551025, 0.810434, 0.198915)
point[4, 22].Init(0.482266, 0.874174, 0.056913)
point[4, 23].Init(0.399335, 0.914133, -0.069943)
point[4, 24].Init(0.303899, 0.936408, -0.175456)
point[5, 0].Init(-0.419463, 0.874872, -0.242177)
point[5, 1].Init(-0.526027, 0.840843, -0.127591)
point[5, 2].Init(-0.617635, 0.786440, 0.006240)
point[5, 3].Init(-0.691524, 0.706116, 0.152297)
point[5, 4].Init(-0.744110, 0.595954, 0.301893)
point[5, 5].Init(-0.771151, 0.455084, 0.445224)
point[5, 6].Init(-0.767991, 0.286709, 0.572702)
point[5, 7].Init(-0.729461, 0.098354, 0.676915)
point[5, 8].Init(-0.649434, -0.098544, 0.754006)
point[5, 9].Init(-0.522934, -0.287521, 0.802416)
point[5, 10].Init(-0.346212, -0.445029, 0.825885)
point[5, 11].Init(-0.122550, -0.539677, 0.832905)
point[5, 12].Init(0.122220, -0.539710, 0.832932)
point[5, 13].Init(0.345847, -0.445268, 0.825910)
point[5, 14].Init(0.522664, -0.288091, 0.802388)
point[5, 15].Init(0.649360, -0.099355, 0.753963)
point[5, 16].Init(0.729563, 0.097471, 0.676933)
point[5, 17].Init(0.768229, 0.285870, 0.572803)
point[5, 18].Init(0.771529, 0.454389, 0.445280)
point[5, 19].Init(0.744541, 0.595404, 0.301914)
point[5, 20].Init(0.691949, 0.705702, 0.152288)
point[5, 21].Init(0.618010, 0.786146, 0.006204)
point[5, 22].Init(0.526322, 0.840647, -0.127659)
point[5, 23].Init(0.419657, 0.874748, -0.242289)
point[6, 0].Init(-0.537578, 0.784015, -0.310371)
point[6, 1].Init(-0.648324, 0.737645, -0.188563)
point[6, 2].Init(-0.741574, 0.668952, -0.050713)
point[6, 3].Init(-0.814138, 0.572726, 0.095730)
point[6, 4].Init(-0.861979, 0.445452, 0.242001)
point[6, 5].Init(-0.879970, 0.286709, 0.378749)
point[6, 6].Init(-0.861638, 0.100529, 0.497467)
point[6, 7].Init(-0.798817, -0.104640, 0.592403)
point[6, 8].Init(-0.682539, -0.313127, 0.660373)
point[6, 9].Init(-0.506393, -0.500953, 0.701863)
point[6, 10].Init(-0.272604, -0.636116, 0.721834)
point[6, 11].Init(-0.000077, -0.686468, 0.727160)
point[6, 12].Init(0.272440, -0.636268, 0.721761)
point[6, 13].Init(0.506244, -0.501283, 0.701735)
point[6, 14].Init(0.682408, -0.313805, 0.660186)
point[6, 15].Init(0.798805, -0.105488, 0.592269)
point[6, 16].Init(0.861747, 0.099653, 0.497454)
point[6, 17].Init(0.880234, 0.285941, 0.378717)
point[6, 18].Init(0.862324, 0.444818, 0.241939)
point[6, 19].Init(0.814498, 0.572226, 0.095654)
point[6, 20].Init(0.741902, 0.668582, -0.050791)
point[6, 21].Init(0.648589, 0.737391, -0.188645)
point[6, 22].Init(0.537754, 0.783854, -0.310472)
point[7, 0].Init(-0.647312, 0.664316, -0.373726)
point[7, 1].Init(-0.754867, 0.607312, -0.247687)
point[7, 2].Init(-0.843007, 0.526592, -0.109727)
point[7, 3].Init(-0.908463, 0.416698, 0.032515)
point[7, 4].Init(-0.946603, 0.273958, 0.169970)
point[7, 5].Init(-0.950956, 0.098354, 0.293275)
point[7, 6].Init(-0.912445, -0.104640, 0.395595)
point[7, 7].Init(-0.819593, -0.323040, 0.473193)
point[7, 8].Init(-0.661696, -0.535180, 0.525110)
point[7, 9].Init(-0.435267, -0.709238, 0.554549)
point[7, 10].Init(-0.152616, -0.809504, 0.566932)
point[7, 11].Init(0.152586, -0.809563, 0.566856)
point[7, 12].Init(0.435255, -0.709380, 0.554376)
point[7, 13].Init(0.661579, -0.535610, 0.524819)
point[7, 14].Init(0.819503, -0.323692, 0.472903)
point[7, 15].Init(0.912447, -0.105390, 0.395390)
point[7, 16].Init(0.951061, 0.097601, 0.293185)
point[7, 17].Init(0.946815, 0.273308, 0.169835)
point[7, 18].Init(0.908716, 0.416158, 0.032363)
point[7, 19].Init(0.843248, 0.526179, -0.109856)
point[7, 20].Init(0.755067, 0.607024, -0.247783)
point[7, 21].Init(0.647448, 0.664140, -0.373804)
point[8, 0].Init(-0.738762, 0.521831, -0.426524)
point[8, 1].Init(-0.836684, 0.457943, -0.300414)
point[8, 2].Init(-0.914323, 0.368932, -0.167040)
point[8, 3].Init(-0.968176, 0.247766, -0.035302)
point[8, 4].Init(-0.992182, 0.091242, 0.085147)
point[8, 5].Init(-0.977705, -0.098544, 0.185424)
point[8, 6].Init(-0.913169, -0.313127, 0.260911)
point[8, 7].Init(-0.785606, -0.535180, 0.310491)
point[8, 8].Init(-0.585341, -0.736999, 0.337947)
point[8, 9].Init(-0.315308, -0.882042, 0.350118)
point[8, 10].Init(0.000045, -0.935572, 0.353135)
point[8, 11].Init(0.315390, -0.882082, 0.349943)
point[8, 12].Init(0.585407, -0.737070, 0.337677)
point[8, 13].Init(0.785540, -0.535487, 0.310128)
point[8, 14].Init(0.913106, -0.313592, 0.260572)
point[8, 15].Init(0.977700, -0.099107, 0.185149)
point[8, 16].Init(0.992251, 0.090659, 0.084959)
point[8, 17].Init(0.968301, 0.247248, -0.035513)
point[8, 18].Init(0.914461, 0.368511, -0.167213)
point[8, 19].Init(0.836805, 0.457647, -0.300526)
point[8, 20].Init(0.738849, 0.521667, -0.426574)
point[9, 0].Init(-0.805540, 0.367161, -0.465079)
point[9, 1].Init(-0.889287, 0.301379, -0.344004)
point[9, 2].Init(-0.952927, 0.207072, -0.221476)
point[9, 3].Init(-0.991207, 0.076832, -0.107732)
point[9, 4].Init(-0.995827, -0.090166, -0.014079)
point[9, 5].Init(-0.956380, -0.287521, 0.051667)
point[9, 6].Init(-0.861028, -0.500953, 0.087619)
point[9, 7].Init(-0.697887, -0.709238, 0.099678)
point[9, 8].Init(-0.460866, -0.882042, 0.098006)
point[9, 9].Init(-0.161821, -0.982388, 0.093427)
point[9, 10].Init(0.162047, -0.982359, 0.093334)
point[9, 11].Init(0.461036, -0.881979, 0.097774)
point[9, 12].Init(0.698006, -0.709159, 0.099397)
point[9, 13].Init(0.861036, -0.500998, 0.087281)
point[9, 14].Init(0.956321, -0.287785, 0.051274)
point[9, 15].Init(0.995786, -0.090561, -0.014434)
point[9, 16].Init(0.991213, 0.076374, -0.108000)
point[9, 17].Init(0.952965, 0.206655, -0.221701)
point[9, 18].Init(0.889340, 0.301082, -0.344129)
point[9, 19].Init(0.805587, 0.367023, -0.465106)
point[10, 0].Init(-0.846372, 0.211831, -0.488653)
point[10, 1].Init(-0.913459, 0.149404, -0.378511)
point[10, 2].Init(-0.960602, 0.051784, -0.273062)
point[10, 3].Init(-0.978879, -0.085344, -0.185777)
point[10, 4].Init(-0.957805, -0.256070, -0.130526)
point[10, 5].Init(-0.888344, -0.445029, -0.113112)
point[10, 6].Init(-0.761429, -0.636116, -0.124834)
point[10, 7].Init(-0.567286, -0.809504, -0.151297)
point[10, 8].Init(-0.305802, -0.935572, -0.176606)
point[10, 9].Init(0.000194, -0.982359, -0.187004)
point[10, 10].Init(0.306124, -0.935441, -0.176741)
point[10, 11].Init(0.567466, -0.809338, -0.151505)
point[10, 12].Init(0.761468, -0.636016, -0.125098)
point[10, 13].Init(0.888290, -0.445043, -0.113476)
point[10, 14].Init(0.957698, -0.256225, -0.131012)
point[10, 15].Init(0.978763, -0.085696, -0.186221)
point[10, 16].Init(0.960540, 0.051325, -0.273364)
point[10, 17].Init(0.913460, 0.149043, -0.378651)
point[10, 18].Init(0.846395, 0.211710, -0.488666)
point[11, 0].Init(-0.863952, 0.069161, -0.498803)
point[11, 1].Init(-0.914357, 0.010245, -0.404778)
point[11, 2].Init(-0.942214, -0.091378, -0.322308)
point[11, 3].Init(-0.933826, -0.231356, -0.272844)
point[11, 4].Init(-0.881026, -0.385655, -0.273979)
point[11, 5].Init(-0.782592, -0.539677, -0.310320)
point[11, 6].Init(-0.629778, -0.686468, -0.363513)
point[11, 7].Init(-0.414619, -0.809563, -0.415571)
point[11, 8].Init(-0.145365, -0.882082, -0.448107)
point[11, 9].Init(0.145843, -0.881978, -0.448156)
point[11, 10].Init(0.414940, -0.809338, -0.415688)
point[11, 11].Init(0.629891, -0.686282, -0.363668)
point[11, 12].Init(0.782554, -0.539604, -0.310543)
point[11, 13].Init(0.880901, -0.385631, -0.274413)
point[11, 14].Init(0.933568, -0.231458, -0.273640)
point[11, 15].Init(0.941981, -0.091937, -0.322831)
point[11, 16].Init(0.914279, 0.009573, -0.404973)
point[11, 17].Init(0.863955, 0.069105, -0.498805)
point[12, 0].Init(-0.864732, -0.054634, -0.499253)
point[12, 1].Init(-0.898697, -0.111854, -0.424066)
point[12, 2].Init(-0.901480, -0.221739, -0.371707)
point[12, 3].Init(-0.856750, -0.334681, -0.392387)
point[12, 4].Init(-0.778709, -0.437948, -0.449238)
point[12, 5].Init(-0.660232, -0.539709, -0.522310)
point[12, 6].Init(-0.488845, -0.636267, -0.596820)
point[12, 7].Init(-0.262477, -0.709380, -0.654130)
point[12, 8].Init(0.000266, -0.737070, -0.675816)
point[12, 9].Init(0.262923, -0.709159, -0.654190)
point[12, 10].Init(0.489072, -0.636016, -0.596902)
point[12, 11].Init(0.660215, -0.539604, -0.522440)
point[12, 12].Init(0.778523, -0.438029, -0.449480)
point[12, 13].Init(0.856453, -0.334649, -0.393062)
point[12, 14].Init(0.900716, -0.221830, -0.373500)
point[12, 15].Init(0.898368, -0.113855, -0.424231)
point[12, 16].Init(0.864736, -0.054543, -0.499256)
point[13, 0].Init(-0.855563, -0.154968, -0.493960)
point[13, 1].Init(-0.875864, -0.220360, -0.429305)
point[13, 2].Init(-0.830026, -0.288446, -0.477343)
point[13, 3].Init(-0.769190, -0.334177, -0.544676)
point[13, 4].Init(-0.678333, -0.385589, -0.625448)
point[13, 5].Init(-0.542338, -0.445267, -0.712465)
point[13, 6].Init(-0.354600, -0.501283, -0.789287)
point[13, 7].Init(-0.123718, -0.535610, -0.835354)
point[13, 8].Init(0.124191, -0.535487, -0.835362)
point[13, 9].Init(0.354930, -0.500998, -0.789320)
point[13, 10].Init(0.542418, -0.445043, -0.712544)
point[13, 11].Init(0.678100, -0.385631, -0.625676)
point[13, 12].Init(0.768629, -0.334649, -0.545179)
point[13, 13].Init(0.829208, -0.288478, -0.478743)
point[13, 14].Init(0.871422, -0.225189, -0.435790)
point[13, 15].Init(0.855668, -0.154194, -0.494020)
point[14, 0].Init(-0.844553, -0.221298, -0.487603)
point[14, 1].Init(-0.817868, -0.229784, -0.527534)
point[14, 2].Init(-0.775523, -0.220851, -0.591430)
point[14, 3].Init(-0.704305, -0.231379, -0.671132)
point[14, 4].Init(-0.592376, -0.256438, -0.763760)
point[14, 5].Init(-0.433558, -0.288090, -0.853833)
point[14, 6].Init(-0.230535, -0.313804, -0.921076)
point[14, 7].Init(0.000205, -0.323692, -0.946162)
point[14, 8].Init(0.230890, -0.313592, -0.921059)
point[14, 9].Init(0.433756, -0.287785, -0.853836)
point[14, 10].Init(0.592309, -0.256224, -0.763884)
point[14, 11].Init(0.703763, -0.231457, -0.671673)
point[14, 12].Init(0.773820, -0.221830, -0.593291)
point[14, 13].Init(0.813119, -0.225191, -0.536775)
point[14, 14].Init(0.845695, -0.215405, -0.488262)
point[15, 0].Init(-0.855563, -0.154968, -0.493960)
point[15, 1].Init(-0.816788, -0.115904, -0.565176)
point[15, 2].Init(-0.750819, -0.092270, -0.654031)
point[15, 3].Init(-0.650711, -0.085970, -0.754443)
point[15, 4].Init(-0.510279, -0.090864, -0.855195)
point[15, 5].Init(-0.328273, -0.099355, -0.939343)
point[15, 6].Init(-0.113518, -0.105488, -0.987920)
point[15, 7].Init(0.113805, -0.105390, -0.987897)
point[15, 8].Init(0.328506, -0.099107, -0.939288)
point[15, 9].Init(0.510393, -0.090560, -0.855159)
point[15, 10].Init(0.650654, -0.085696, -0.754523)
point[15, 11].Init(0.750570, -0.091937, -0.654364)
point[15, 12].Init(0.816579, -0.113855, -0.565894)
point[15, 13].Init(0.855668, -0.154194, -0.494020)
point[16, 0].Init(-0.864732, -0.054634, -0.499253)
point[16, 1].Init(-0.807923, 0.008998, -0.589219)
point[16, 2].Init(-0.717039, 0.051050, -0.695161)
point[16, 3].Init(-0.589068, 0.076118, -0.804491)
point[16, 4].Init(-0.422404, 0.090435, -0.901885)
point[16, 5].Init(-0.221460, 0.097471, -0.970286)
point[16, 6].Init(0.000065, 0.099653, -0.995022)
point[16, 7].Init(0.221624, 0.097601, -0.970235)
point[16, 8].Init(0.422549, 0.090659, -0.901794)
point[16, 9].Init(0.589138, 0.076374, -0.804415)
point[16, 10].Init(0.717010, 0.051325, -0.695170)
point[16, 11].Init(0.807856, 0.009573, -0.589302)
point[16, 12].Init(0.864736, -0.054543, -0.499256)
point[17, 0].Init(-0.863952, 0.069161, -0.498803)
point[17, 1].Init(-0.784623, 0.148892, -0.601829)
point[17, 2].Init(-0.668387, 0.206487, -0.714578)
point[17, 3].Init(-0.514740, 0.247069, -0.820975)
point[17, 4].Init(-0.326114, 0.273168, -0.905002)
point[17, 5].Init(-0.111948, 0.285870, -0.951707)
point[17, 6].Init(0.112138, 0.285941, -0.951663)
point[17, 7].Init(0.326326, 0.273308, -0.904883)
point[17, 8].Init(0.514906, 0.247248, -0.820817)
point[17, 9].Init(0.668481, 0.206655, -0.714441)
point[17, 10].Init(0.784652, 0.149043, -0.601754)
point[17, 11].Init(0.863955, 0.069105, -0.498805)
point[18, 0].Init(-0.846372, 0.211831, -0.488653)
point[18, 1].Init(-0.742614, 0.301067, -0.598233)
point[18, 2].Init(-0.601895, 0.368441, -0.708501)
point[18, 3].Init(-0.426144, 0.416056, -0.803305)
point[18, 4].Init(-0.221374, 0.444763, -0.867859)
point[18, 5].Init(0.000140, 0.454389, -0.890803)
point[18, 6].Init(0.221637, 0.444818, -0.867764)
point[18, 7].Init(0.426330, 0.416159, -0.803153)
point[18, 8].Init(0.602041, 0.368511, -0.708340)
point[18, 9].Init(0.742694, 0.301082, -0.598127)
point[18, 10].Init(0.846395, 0.211710, -0.488666)
point[19, 0].Init(-0.805540, 0.367161, -0.465079)
point[19, 1].Init(-0.678553, 0.457703, -0.574520)
point[19, 2].Init(-0.516575, 0.526189, -0.675482)
point[19, 3].Init(-0.324154, 0.572217, -0.753321)
point[19, 4].Init(-0.110501, 0.595400, -0.795794)
point[19, 5].Init(0.110805, 0.595404, -0.795749)
point[19, 6].Init(0.324411, 0.572226, -0.753203)
point[19, 7].Init(0.516761, 0.526179, -0.675346)
point[19, 8].Init(0.678666, 0.457647, -0.574432)
point[19, 9].Init(0.805587, 0.367023, -0.465106)
point[20, 0].Init(-0.738762, 0.521831, -0.426524)
point[20, 1].Init(-0.591964, 0.607129, -0.530069)
point[20, 2].Init(-0.414707, 0.668644, -0.617198)
point[20, 3].Init(-0.213800, 0.705730, -0.675452)
point[20, 4].Init(0.000156, 0.718110, -0.695930)
point[20, 5].Init(0.214089, 0.705702, -0.675389)
point[20, 6].Init(0.414938, 0.668582, -0.617110)
point[20, 7].Init(0.592120, 0.607024, -0.530016)
point[20, 8].Init(0.738849, 0.521667, -0.426574)
point[21, 0].Init(-0.647312, 0.664316, -0.373726)
point[21, 1].Init(-0.487468, 0.737516, -0.467381)
point[21, 2].Init(-0.303375, 0.786221, -0.538350)
point[21, 3].Init(-0.102953, 0.810460, -0.576677)
point[21, 4].Init(0.103247, 0.810434, -0.576660)
point[21, 5].Init(0.303633, 0.786146, -0.538314)
point[21, 6].Init(0.487666, 0.737391, -0.467372)
point[21, 7].Init(0.647448, 0.664140, -0.373804)
point[22, 0].Init(-0.537578, 0.784015, -0.310371)
point[22, 1].Init(-0.373494, 0.840760, -0.391951)
point[22, 2].Init(-0.191583, 0.874232, -0.446110)
point[22, 3].Init(0.000138, 0.885244, -0.465127)
point[22, 4].Init(0.191845, 0.874174, -0.446111)
point[22, 5].Init(0.373717, 0.840647, -0.391979)
point[22, 6].Init(0.537754, 0.783854, -0.310472)
point[23, 0].Init(-0.419463, 0.874872, -0.242177)
point[23, 1].Init(-0.260017, 0.914213, -0.310815)
point[23, 2].Init(-0.088117, 0.933302, -0.348112)
point[23, 3].Init(0.088358, 0.933275, -0.348124)
point[23, 4].Init(0.260239, 0.914133, -0.310862)
point[23, 5].Init(0.419657, 0.874748, -0.242289)
point[24, 0].Init(-0.303716, 0.936487, -0.175351)
point[24, 1].Init(-0.156119, 0.960423, -0.230684)
point[24, 2].Init(0.000101, 0.968121, -0.250482)
point[24, 3].Init(0.156315, 0.960380, -0.230729)
point[24, 4].Init(0.303899, 0.936408, -0.175456)
point[25, 0].Init(-0.199591, 0.973080, -0.115234)
point[25, 1].Init(-0.068350, 0.985322, -0.156424)
point[25, 2].Init(0.068499, 0.985308, -0.156449)
point[25, 3].Init(0.199737, 0.973040, -0.115318)
point[26, 0].Init(-0.113945, 0.991307, -0.065786)
point[26, 1].Init(0.000042, 0.995956, -0.089839)
point[26, 2].Init(0.114030, 0.991294, -0.065835)
point[27, 0].Init(-0.048990, 0.998399, -0.028285)
point[27, 1].Init(0.049018, 0.998397, -0.028300)
point[28, 0].Init(0.000000, 1.000000, -0.000000)
Here is the inner loop:
Code:
              float magnitude = 1
              int ij = 0

              posit.x = real(zri)     ; convert z to vector for ease of use
              posit.y = imag(zri)
              posit.z = zj
              ij = 0
              repeat
                magnitude = posit.Dot(normals[ij])
              if (magnitude > 0) ; on wrong side of triangle
                magnitude = posit.Magnitude()
                ; super simple way to get barycentric coordinates of triangle
                bary.z = crosses[ij*3 + 0].Dot(posit)
                bary.y = crosses[ij*3 + 1].Dot(posit)
                bary.x = crosses[ij*3 + 2].Dot(posit)
              if (bary.x >= 0 && bary.y >= 0 && bary.z >= 0)
                bary.Divide(bary.x+bary.y+bary.z)
                ; now we use barycentric coordinates to do interpolated table lookup
                float il = bary.x*28
                float jl = bary.y*28
                int floorI = floor(il)
                int floorJ = floor(jl)
                float fi = il - floorI
                float fj = jl - floorJ
                if (fi + fj) < 1
                  posit.Multiply(point[floorI, floorJ], (1 - (fi + fj)))
                  temp1.Multiply(point[floorI, floorJ+1], fj)
                  temp2.Multiply(point[floorI+1, floorJ], fi)
                else
                  posit.Multiply(point[floorI+1, floorJ+1], (1 - ((1-fi) + (1-fj))))
                  temp1.Multiply(point[floorI, floorJ+1], (1-fi))
                  temp2.Multiply(point[floorI+1, floorJ], (1-fj))
                endif
                posit.AddEquals(temp1)
                posit.AddEquals(temp2)

                ; Z^2 + c
                magnitude = magnitude*magnitude
                posit.MultiplyEquals(magnitude)
                posit.AddEquals(C)
                ij=10 ; break
              endif
              endif
              until (ij = ij+1)>=4
              zri = posit.x + flip(posit.y)
              zj = posit.z
And to get this fractal: "http://www.fractalforums.com/3d-fractal-generation/a-new-tetrahedral-mandelbulb/?action=post;quote=11415;num_replies=4;sesc=aee003da38f141169bfe35f4f08fee04" just change the last two lines to:
Code:
zri = -posit.x + flip(posit.y)
              zj = -posit.z
It would be great to see some other people's renderings of these, or any tips on how I can improve the look of my renders using UltraFractal.
Logged
kram1032
Fractal Senior
******
Posts: 1863


« Reply #17 on: January 16, 2010, 07:14:11 PM »

puh, not surprising but that looks quite a bit more complex than the spherical version... smiley
Logged
Tglad
Fractal Molossus
**
Posts: 703


WWW
« Reply #18 on: January 21, 2010, 12:59:59 AM »

Yes, there is almost certainly no analytical function for the mapping so the inner loop is a table lookup. Would probably need a bezier-patch interpolation for more accurate zooms.

The latest mapping is very close to optimal for a spherical mapping, and strangely it results in the fractal here (http://www.fractalforums.com/3d-fractal-generation/a-new-tetrahedral-mandelbulb/?action=post;quote=11468;num_replies=7;sesc=3eb172cbad5c958d490380638fbf323b) and the alien fractal above becoming the same thing, so if you rotate the space 180 around y each iteration you get the same shape just upside-down. Spot the difference.

Using a more accurate measure for stretch (the post-mapping long length over short length) the average stretch of this mapping is 1.5. Mandelbrot is 1, mandelbulbs are infinity.


* spotDiff.jpg (86.31 KB, 868x369 - viewed 586 times.)

* surface.jpg (256.17 KB, 796x796 - viewed 574 times.)
Logged
kram1032
Fractal Senior
******
Posts: 1863


« Reply #19 on: March 06, 2010, 02:48:25 PM »

I like that surface render however I wouldn't dare walking on a planet with that structure barefeeted, smiley
Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #20 on: February 12, 2015, 10:28:04 AM »

I wonder if is anyone able to simplify the formula a bit?
For example reduce or kill lookup table cheesy
(Or even better simplify it a lot ... cheesy)
It's too complicated to implement for me as is embarrass
« Last Edit: February 12, 2015, 10:32:43 AM by DarkBeam » Logged

No sweat, guardian of wisdom!
Tglad
Fractal Molossus
**
Posts: 703


WWW
« Reply #21 on: February 13, 2015, 03:55:26 AM »

There might be a function that does such a scaling of a sphere surface triangle... possibly a holomorphic one (a complex polynomial). But I don't know what it is, if it exists.
Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #22 on: February 13, 2015, 10:15:00 AM »

Okay sir but then I ask you, how did you find those numbers?
Are they sines of some angle? Square roots? Randoms?

Why ...
point[0, 19].Init(0.000000, 0.367160, 0.930158)
and is there a relation with others?

Please be patient smiley

Thanks a lot smiley
Logged

No sweat, guardian of wisdom!
Tglad
Fractal Molossus
**
Posts: 703


WWW
« Reply #23 on: February 13, 2015, 11:15:29 AM »

I am folding a tetrahedron (which is projected onto a sphere) onto itself (on the surface of a sphere) as shown in the video on the first page.
So each of the 4 triangles (on the sphere) expand into a larger triangle 4 times the area. Since I don't know a function that does that conformally, I wrote a program that meshes such a triangle, expands it and then tries to maintain the mesh shape... so something like what would happen if the triangle was made of rubber. The program spat out the transformed mesh vertices, which approximates the transform.
The main goal of the transform is to keep the expanded shape as conformal as possible.

The bigger goal was to make a sphere to sphere folding that was as conformal as possible (given that a fully conformal one is impossible).
One problem is that the results are inevitably non-smooth at the triangle boundaries... though still continuous.
Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #24 on: February 13, 2015, 05:59:37 PM »

Ok at least now it's more clear. Thanks again smiley
Logged

No sweat, guardian of wisdom!
hgjf2
Fractal Phenom
******
Posts: 456


« Reply #25 on: February 14, 2015, 01:43:26 PM »

More patience need. The new FRACTALFORUMS competition begin may 2015, not march 2015.
 canadian laugh 
Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #26 on: February 14, 2015, 03:55:08 PM »

Uh, even a lifetime won't be enough since to hardcode a 2d array (of floats!) is way beyond my assembly knowledge cheesy maybe doable with some dirty tricks but ehh tongue stuck out
Logged

No sweat, guardian of wisdom!
1990winfractal
Forums Newbie
*
Posts: 8



« Reply #27 on: April 11, 2015, 02:55:55 AM »

looks cool print it in on a 3d printer then wow
Logged

I am new to this form but not to fractals I love them I wish to fly in one with out a computers help one day
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