Creative coding using strange attractors creates new species.

New species found in the code!

It's a creative coding artwork made with the 'Processing'.

When I was playing with De Jong attractors, I found this formula occasionally makes a shape like a jellyfish.

x1 = sin(a * y0) - cos(b * x0) + sin(c * y0) - cos(d * x0);
y1 = sin(c * x0) - cos(d * y0) + sin(a * x0) - cos(b * y0);

But it is a very rare thing to make a shape. So I collected the right parameters by hand.

 

The 'Processing' example code.

Please feel free to use this example code under the terms of the GPL.
To see other works based on my code is my pleasure. And my honor.

/**
 * Is There Life Out There.
 * 
 * draw shape like a jellyfish.
 * 
 * @author @deconbatch
 * @version 0.2
 * Processing 3.2.1
 * created 0.1 2018.06.10
 * updated 0.2 2019.04.20 : use ArrayList to avoid duplicate parameter choosing.
 */

class Dna {

  ArrayList<float[]> dnaList;
  float     hueBase;

  Dna() {

    hueBase = random(360);

    float[][] dnas = {

      // Big Oval
      {1.1849121, 0.9095465, 0.8848125, -1.5089083},
      {0.93254054, -0.94148505, 0.6806822, 0.954301},
      {-0.7303996, 0.96663284, -0.7082044, 1.3012471},
      {1.4183311, -0.7739556, 0.8932247, -1.6508615},
      {1.0061936, 0.74306273, 0.57587314, -0.94024205},
      {-1.9807187, -0.98512995, 0.90511715, -1.1383728},
      {-0.39753437, -1.8430407, -1.5989869, 1.97157},
      {1.9872496,  -1.2223938,  0.75760174,  0.8577473},
      {-1.0212829, 1.8065041, -1.065195, -1.2893174},
      {-0.6682879, 1.1899773, -1.0501943, 0.97608304},
      {-0.95598626, -0.67845774, -0.5897205, -0.7853384},
      {-0.6002734, 1.6509838, 1.8099892, -1.0964627},
      {1.2138364, 1.8424428, 1.0873783, -1.5026784},
      {-0.6992879, -1.4193265, -1.2935817, -1.3413115},
      {0.35385942, -1.1933832, -1.7852755, -1.5394485},
      {-1.0097787, -1.7620895, -1.0556421, -1.9306729},
      {1.0139189, -1.6474402, -1.8250722, -1.7590555},
      {1.7736316, -0.99833524, 1.2907677, -1.2401295},
      {1.182705, 0.96390736, 1.9748241, -0.812695},

      // Big Round
      {-1.2797397, -0.87958217, -0.67786217, 1.278327},
      {1.8544704, -0.5590235, 0.8619487, 1.7108389},
      {-1.2070764, 0.80302453, -0.7602345, -1.4232765},
      {1.0074179, -1.1320828, 1.2655354, 0.9310633},

      // Big Rect
      {-0.8031204, 1.5344392, -0.24503994, -1.1079564},
      {-1.801286, -0.59856784, -1.4183506, 0.8612491},
      {1.0504521, -0.8799838, 0.59731424, 1.6561341},
      {-1.5126178, 0.96751165, -1.4654857, 0.39162695},
      {0.4748206, 1.4318291, 0.7834574, -0.78170085},
      {-1.882327, 0.7454052, -1.8220787, 0.59406745},
      {1.0037864, 1.04777, 0.3759683, -1.353185},
      {-0.2930424, -1.2779334, -0.25360557, -1.7757171},
      {0.17204833, -1.7023778, 0.56470084, 1.963506},
      {-0.6, -1.4539845, -0.2113738, -1.7798028},

      // Midium Oval
      {-1.9465947, 1.7589694, 1.389837, 1.7326984},
      {-1.730861, 0.95459366, -0.83617437, 0.24412167},
      {-1.5446866, -1.2540207, -0.31753004, -0.120238066},
      {-1.5951449, -1.0492635, -0.2364794, -0.29167426},
      {1.8142333, 1.6540196, -0.48046672, 0.13015974},
      {-1.6773063, -1.1689367, -0.45730066, -0.26610088},
      {1.4310315, -0.77496755, 0.018437862, -1.8364917},
      {1.6609163, 0.78412163, 0.96825004, -1.3146304},
      {1.3210852, 0.754848, 0.32918036, 1.8211994},
      {1.4341059, -0.9974872, -0.9644693, 1.3870964},
      {1.9581228, -0.78601146, 0.054947495, 1.7886631},
      {-1.7919123, -0.91870475, 0.33036876, -1.953738},
      {1.5484775, -0.51683605, 0.6441766, -1.6338},
      {1.6152817, -0.5806426, -0.7122184, 1.7577422},
      {-1.8441538, -0.22325456, -0.31500757, 1.241184},
      {-0.8945819, -1.3282559, -1.8884094, 0.101511955},
      {-0.4305334, 1.2295167, -1.4078912, 0.63412094},
      {0.69905794, -1.3268771, 1.8773909, 0.88926256},
      {0.9608946, 1.526935, 1.2917542, 0.6744671},
      {0.5857947, -1.4809624, 1.1994996, -0.8638495},
      {-0.5692072, -1.6045585, 1.5878702, -0.16901553},
      {-0.443424, 1.4503305, 1.5551313, -0.63595104},
      {-0.86442184, -1.4106861, -1.1665003, 0.19020247},
      {0.13074791, -1.6833956, -1.5791191, 0.90134645},
      {-0.9612212, -1.265603, -0.22904015, 0.5489944},
      {-0.10190797, -1.0497519, -0.7050872, -0.97304344},
      {-0.76477623, -0.6079043, -1.1919898, -0.3023368},
      {0.8834467, -0.9597125, -0.03519106, 1.0781043},
      {-0.8442018, 0.8730582, -0.0036774874, 1.2375482},
      {-0.055605173, -0.9984672, -0.9284352, -1.3113402},
      {1.7263665, -0.13234115, 0.9308158, -1.6337785},
      {1.0927025, -0.6339817, 0.39143145, 1.696924},
      {-1.6324822, -0.1511184, -0.50280654, -1.3972737},
      {1.8253258, -0.32701004, -0.7343477, 1.7417251},
      {1.3174697, -0.3380171, 0.84481204, 1.5128938},
      {-1.3373101, 0.7658353, -0.82038116, 1.0360359},
      {1.4618424, -0.30335462, 0.6859448, 1.4082092},
      {-1.4713892, -0.0446918, -0.38030994, 1.281949},
      {1.9282612, -0.56053495, 0.8357527, 1.7882413},
      {1.6614151, -0.9171884, 0.44198537, 0.97992384},
      {-1.895432, 0.8124887, -0.5809063, 1.4251728},
      {-1.3358968, 0.5784098, -0.656173, -1.7915728},
      {1.573155, -0.97604156, -0.49153805, -1.7673008},
      {1.3982303, 0.60875034, 0.8057699, -1.7793968},
      {1.5713205, -0.38313913, 0.8031683, 1.5579807},
      {1.689565, -0.9906876, -0.5665313, -1.7728505},
      {1.7615415, -0.089163184, -0.45041764, 1.7219753},
      {1.7335646, -0.6859281, 0.45778573, -1.8296082},
      {-1.4305836, -1.5645888, 0.13956404, 0.83102083},
      {-1.6462411, 1.0734643, -0.34455848, 0.72796464},
      {-1.976744, 1.657812, -0.9153664, -0.1308614},
      {-1.7427628, 1.7868494, 0.2976929, 0.24575019},
      {1.9509783, -1.9764297, -0.8395766, 0.7449101},
      {1.3177984, 0.1433264, 0.88074243, 0.8908167},
      {-0.7601371, -1.3737268, -1.2622802, 0.20960975},
      {-0.574955, -1.845849, -1.4538138, -0.8027086},
      {1.8942447, -1.3003662, -1.2996788, 1.6064854},
      {1.0643706, -1.1258738, -0.14309597, -1.1692727},
      {-0.74886227, 1.774987, -1.8375673, 0.29043174},
      {1.5574002, 1.8453715, 0.47246575, -0.78352594},
      {-1.9145522, -1.5549593, 1.3220832, 1.9297299},
      {-0.2231934, -1.1355813, 1.4720156, -1.5030069},
      {1.3413672,  1.848628,  0.07917428,  0.97517014},
      {0.2746935, -1.9293225, -1.9918222, -1.1164157},
      {-1.7496462, 0.44626546, 0.23361754, -1.7961285},
      {1.048422, -1.5934495, -1.8014144, 1.8853657},
      {-1.0119417, 0.9379139, 1.3950387, 1.7682558},
      {-1.3168592, -0.9006443, -0.8308315, -0.11977494},
      {-1.0619688, 0.8422779, -0.0039972067, 0.8684653},
      {-1.6818013, 0.8691511, -0.55203354, 0.69016147},
      {1.6240658, -1.7089772, 0.34328735, 0.56289184},
      {-1.4741437, 1.5583007, -0.2769848, -0.54520416},
      {1.6444424, -1.8289783, 0.50425446, 0.6019844},
      {-1.683015, 1.6719978, 0.29515135, -0.844509},
      {-1.4194199, 1.7347983, 0.6168746, -0.9466268},
      {-1.667172, -0.88657916, 0.051608205, 1.7629937},
      {-1.6650431, 0.37775326, 0.33541465, 1.8434201},
      {1.4223164, 0.55100656, 0.49716485, 1.6428655},
      {-1.5163244, 0.4479139, 0.036285758, -1.2978761},
      {-1.8220417, 0.69640577, 0.6617968, -1.7121897},
      
      // Midium Round
      {1.6460918, 0.7578703, 0.039756656, 1.6673663},
      {1.5850691, -0.77938485, -0.0088124275, -1.9552058},
      {-1.918999, 0.29473996, -0.1918658, 1.6541685},
      {-1.5164984, 0.9213618, -0.24812913, 1.714503},
      {-0.8824867, -1.5992742, -1.5625699, 0.66312945},
      {0.11071241, -1.9701986, -1.7158189, 0.745958},
      {0.08696866, 1.6187843, 1.742263, -0.6025481},
      {-0.910071, -1.3847178, -1.8182942, 0.4131807},
      {0.8275225, -1.6412234, 1.7822884, -0.67995834},
      {1.470601, -0.733212, 0.018205523, 1.6027497},
      {-1.8664721, -0.61742485, -0.5398445, 1.617141},
      {-1.3899937, -0.5352411, -0.048462868, 1.4123926},
      {1.521275, 0.26149035, 0.96596193, -1.1724942},
      {-1.8529294, 1.5464774, -0.99372435, -0.4649179},

      // Midium Rect
      {1.7804039, -0.122492075, 1.8946829, -1.3945198},
      {1.2306535, 1.8258467, 0.2621975, 0.86369896},
      {1.0511895, 1.7504905, 0.19852757, -0.6846205},
      {0.08815479, 1.7238736, -0.93964684, 1.2135742},
      {-0.08503556, -1.2355243, 0.61759496, -1.1704419},
      {-1.5153672, -1.6223017, 1.128174, 1.8484828},
      {1.6109155, -0.922786, -1.8774289, 1.3826112},
      {-1.5303104, 1.4835638, 1.955475, -1.3815746},
      {1.1972777, -1.6909255, -1.5501943, -1.0349056},
      {-1.3127844, -1.5479167, 1.8265626, -1.2843121},
      {1.8529391, 1.6386267, -1.4421663, -0.953791},
      {1.8401479, -1.6835139, -1.2599678, -1.5183538},
      {1.8532482, -1.802887, -1.412819, 1.2291515},
      {-1.2992105, 1.0856447, 1.6794627, 1.5119364},
      {0.51639056, 1.80406, -1.3071277, 1.2810354},
      {1.1143556, -1.8553946, -1.4474993, 1.5575024},
      {-0.0022146702, -1.2386405, 0.25423622, 1.1112525},
      {0.029160976, -1.7689974, -1.3037977, 1.5815482},
      {-1.1889801, -1.3818119, 0.24878383, -1.8614237},

      // Midium Long
      {1.6476917, 0.535202, 1.0525138, -0.79539895},
      {1.9704357, -1.7049251, -1.5149391, -1.141536},
      {1.7476617, 0.61932206, -0.22354555, -1.3771973},
      {1.718496, 1.5134321, -0.3304677, -0.55999243},
      {1.6859903, -1.1094145, 0.95170677, 0.03142214},
      {1.6628836, 0.7035632, -0.95645726, -1.727245},
      {1.472203, -0.898963, -0.9679501, -1.400193},
      {1.8290453, 0.7760278, -0.4744134, -1.4932538},
      {-1.2330908, 0.34469938, -0.49853098, -1.5406578},
      {1.715469, 0.04186046, -0.3836038, 1.1650492},
      {1.6984602, 0.68749607, -0.48256612, -1.3140318},
      {1.9247553, -1.0537516, 0.9806514, 0.4848814},
      {-0.4760959, 1.1698606, 1.6613967, -0.57288},
      {1.5750878, -0.3097632, 1.1259277, -0.45882177},
      {1.4875183, 0.23624885, 1.2554035, 0.89778733},

      // Midium Jellyfish
      {-1.337883, 0.7986244, -0.7287731, 0.37230742},
      {-1.3406851, -0.28214872, -0.5861671, -1.2162886},
      {-1.4316964, 0.3185227, -0.6400242, 1.1442337},
      {-1.0625868, -1.21026, -0.6712706, -0.46117342},
      {0.9189794, -1.1565351, 0.34334147, -0.79307437},
      {-1.0536402, -1.3200992, -0.5447396, 0.4220116},
      {-1.0032872, 1.2655714, -0.26810575, -0.52376616},
      {-1.6401721, 0.49672115, -0.86271167, 1.0925014},
      {-1.089398, 0.050195098, -0.7560389, 0.9639907},
      {-1.5165274, 0.45882142, -0.763324, 1.0880857},
      {1.2159896, 0.71907735, 1.7588662, -0.8050928},
      {-0.67342365, -1.1019428, -1.1452117, 0.29434526},
      {0.032641053, 0.7753694, -0.7903284, 0.91263294},
      {-1.7141302, -0.5167841, -0.91756153, -1.0736923},
      {-1.5073094, -0.18403065, -0.4235146, -1.1396475},
      {-1.5907371, -0.4164865, -0.29266846, 1.2113163},
      {-1.6313002, -0.91586375, -0.8607278, 1.0326489},
      {-1.7225821, 0.77831185, -0.19446528, -1.3474123},
      {-1.0811185, -0.547776, -0.11046791, -1.1848762},
      {-1.6915625, 0.75691473, -0.17169261, 1.5456556},
      {1.8049909, 0.30004144, -0.57724154, -1.8308672},
      {-1.0283998, -0.59822416, -0.11413801, 1.1734248},
      {-1.3578292, -0.45746374, -0.51071835, 1.1609248},
      {-1.1390313, -0.51329076, -0.54873264, 1.2952505},
      {-1.1412683, -0.8699349, -0.84301496, 0.52159405},
      {-1.1155736, 0.5643594, -0.72264886, -0.5976572},
      {-1.994314, 1.1001192, 1.0783195, 0.97809243},
      {-1.070556, 1.283265, -1.8349171, -0.92877495},
      {-1.18695, 1.6172869, -0.21208334, 0.9708407},
      {1.0284084, 0.90697336, 1.9091114, -0.48130915},
      {-0.3080871,  1.3259976,  -1.1706066,  0.5073533},
      {-0.69023013, -0.1302743, -1.8621659, -1.0325127},
      {-0.6484239, 1.2749679, -1.1394744, -0.44516706},
      {1.0016232, -1.622549, 1.5726357, 0.032066584},
      {-0.52549577, -0.67942905, -1.3125789, -0.5507343},
      {1.8917582, 0.15021777, -0.6037681, -1.8276622},
      {-1.568748, 0.9688648, -0.3640505, 0.50801337},
      {-1.0605584, 0.43145335, -0.28898394, 1.2417426},
      {1.4691906, -0.29476404, 0.3509971, -1.6438289},

      // Small Oval
      {-1.2209034, -1.9364693, 1.624037, -0.89463496},
      {-1.7154304, 0.30037725, 0.5552659, 1.8298564},
      {0.2816223, 1.7652395, -1.9630059, -0.0074948072},
      {-1.0999322, -0.7065116, 0.19727302, -1.6968937},
      {-1.428522, 1.4215118, -0.19567788, -0.28131342},
      {1.9320453, 0.29188907, -0.34393072, -1.694332},
      {1.5224934, -0.45708573, -0.1851772, 1.6764568},
      {1.5854416, 0.14847529, -0.37849796, -1.6866535},
      {-1.582921, -0.4308331, -0.003947735, 1.4218943},
      {1.4534781, -0.63194084, -0.12436688, 1.8669703},
      {1.5655034, 0.1567384, 0.38440907, -1.4910831},
      {1.3665309, 0.5035374, 0.58554673, 1.287977},
      {1.4358952, 0.2323507, 0.18323982, -1.3870456},
      {1.5138388, 0.56453073, 0.067702174, 1.6984639},
      {1.9535902, -0.309726, -0.1853993, 1.8736959},
      {0.18226886, 0.4491577, 1.4308531, -1.5269957},
      {1.5496799, 1.6239533, -0.07193291, 0.44251096},
      {1.6603223, -1.7008573, -0.9214597, -0.41860712},
      {-1.9872514, -1.949431, 0.28242278, -0.082980275},
      {1.2246487, 0.9815867, -0.33256805, -1.6527531},

      // Small Rect
      {1.066198, -0.9836912, -0.4956653, -1.4955009},
      {-1.8875654, 1.0541544, 1.6701783, 1.3673763},
      {1.021009, -1.2431176, -0.67271996, 0.87261355},
      {0.88199544, -1.416499, -1.2734511, -0.9998332},
      {-0.4624852, 0.8432921, 0.92639494, -1.5932047},
      {-1.1976266, -0.7914636, 0.8764535, -1.6663439},
      {-0.68983793, -0.79637814, 1.1002138, 1.9818056},
      {1.0020864, 1.3080509, -0.6799123, -0.81804633},
      {-0.40744567, 1.3564913, 0.843601, -0.79346967},
      {-0.5327811, 0.9770564, 0.97481287, 1.1749895},
      {-0.2816894,  -1.2925198,  -0.038594007,  0.6182854},
      {-1.9844887, -0.092148066, 1.1646574, -0.2779312},
      {-0.6, -1.1537788, 1.0042028, 1.1472845},

      // Small Jellyfish
      {1.5601017, 1.4882118, 0.42056704, -0.14340937},
      {1.1732215, 0.6332152, -0.5784129, 1.6936051},
      {1.5162741, 0.27948642, -0.69752645, 1.7646685},
      {1.58486, -0.27417886, 0.649879, -1.4235511},
      {-1.4250407, -1.1277831, -0.15991056, 0.33121157},
      {-1.4276958, 0.09797263, -0.3287897, 0.99054456},
      {0.40637827, -0.23529363, 1.9798067, -0.92299604},
      {-1.8401535, -0.99712443, -0.62072957, -0.19675004},

      // Star Wars Rebel Alliance
      {-1.5568858, -1.5821334, -1.2908077, -1.0470141},

      // Star Wars Empire
      {1.5798012, 1.2170191, 0.44912982, 0.9654827},

    };

    dnaList = new ArrayList<float[]>();
    for (float[] dna : dnas) {
      dnaList.add(dna);
    };

  }

  void changeHue() {
    hueBase = (hueBase + 120) % 360;
  }
  
  float getHue() {
    return hueBase;
  }

  float[] getRandomDna() {
    int choice = floor(random(dnaList.size()));
    float[] dnaChose = dnaList.get(choice);
    dnaList.remove(choice);
    return dnaChose;
  }

}


/* ---------------------------------------------------------------------- */
Dna dna;

void setup() {

  size(980, 980);
  colorMode(HSB, 360, 100, 100, 100);
  blendMode(SCREEN);
  smooth();
  noStroke();
  textSize(20);

  dna = new Dna();
  
}

void draw() {

  float[] rndDna = dna.getRandomDna();
  dna.changeHue();

  background(dna.getHue(), 100.0, 10.0, 100.0);
  translate(width / 2, height / 2);

  /*
    fill(0, 0, 100, 100);
    text("a=", 240, 340);  text(rndDna[0], 280, 340);
    text("b=", 240, 360);  text(rndDna[1], 280, 360);
    text("c=", 240, 380);  text(rndDna[2], 280, 380);
    text("d=", 240, 400);  text(rndDna[3], 280, 400);

    println(frameCount, "{", rndDna[0], ",", rndDna[1], ",", rndDna[2], ",", rndDna[3], "},");
    println();
  */

  float briMax = 50.0;
  
  float prevX = 0.0;
  float prevY = 0.0;
  float prevZ = 0.0;

  for (int i = 0; i < 2000000; ++i) {

    float x = sin(rndDna[0] * prevY) - cos(rndDna[1] * prevX) + sin(rndDna[2] * prevY) - cos(rndDna[3] * prevX);
    float y = sin(rndDna[2] * prevX) - cos(rndDna[3] * prevY) + sin(rndDna[0] * prevX) - cos(rndDna[1] * prevY);
    float z = sin(rndDna[0] * prevX) - cos(rndDna[1] * prevZ) + sin(rndDna[0] * prevY) - cos(rndDna[1] * prevZ);
    
    float size = 1;
    float hueApply = (dna.getHue() + map(z, -4.0, 4.0, 0.0, 90.0)) % 360;
    float briApply = map(z, -4.0, 4.0, briMax, 3.0);
    float alpApply = log(briMax) / log(briApply) * 35.0;

    fill(hueApply, 40, briApply, alpApply);
    pushMatrix();
    translate(x * width / 10.0, y * height / 10.0);
    ellipse(0, 0, size, size);
    popMatrix();

    prevX = x;
    prevY = y;
    prevZ = z;

  }

  saveFrame("frames/####.png");
  if (frameCount >= 3) {
    exit();
  }

}


/*
Copyright (C) 2018- deconbatch

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>
*/

Yet another example images.