{"id":442,"date":"2024-01-25T11:11:56","date_gmt":"2024-01-25T02:11:56","guid":{"rendered":"https:\/\/barbegenerativediary.com\/en\/?p=442"},"modified":"2024-01-25T11:11:56","modified_gmt":"2024-01-25T02:11:56","slug":"the-strange-attractors-code-and-equations","status":"publish","type":"post","link":"https:\/\/barbegenerativediary.com\/en\/artworks\/the-strange-attractors-code-and-equations\/","title":{"rendered":"The Strange Attractors | Code and Equations"},"content":{"rendered":"\n<p>This article introduces examples of works using Strange Attractor, as well as some sample code and output results.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Index<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"#TheStrangeAttractors-1\" title=\"\"><strong>Sample Graphic of barbe_generative_diary<\/strong><\/a><\/li>\n\n\n\n<li><strong><a href=\"#TheStrangeAttractors-2\" title=\"\">Sample Code with openFrameworks<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#TheStrangeAttractors-3\" title=\"\">The Strange Attractors<\/a><\/strong><br><a href=\"#TheStrangeAttractors-3-1\" title=\"\">The Aizawa Attractor<\/a><br><a href=\"#TheStrangeAttractors-3-2\" title=\"\">The Chua Attractor<\/a><br><a href=\"#TheStrangeAttractors-3-3\" title=\"\">The Halvorsen Attractor<\/a><br><a href=\"#TheStrangeAttractors-3-4\" title=\"\">The Lorenz Attractor<\/a><br><a href=\"#TheStrangeAttractors-3-5\" title=\"\">The Newton &#8211; Leipnik Attractor<\/a><br><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TheStrangeAttractors-1\">Sample Graphic of barbe_generative_diary<\/h2>\n\n\n\n<p>This is a barbe_generative_diary&#8217;s graphic sample using Strange Attractor.<\/p>\n\n\n\n<blockquote class=\"instagram-media\" data-instgrm-permalink=\"https:\/\/www.instagram.com\/p\/Cnyly08uA1_\/?utm_source=ig_embed&amp;utm_campaign=loading\" data-instgrm-version=\"14\" style=\" background:#FFF; border:0; border-radius:3px; box-shadow:0 0 1px 0 rgba(0,0,0,0.5),0 1px 10px 0 rgba(0,0,0,0.15); margin: 1px; max-width:540px; min-width:326px; padding:0; width:99.375%; width:-webkit-calc(100% - 2px); width:calc(100% - 2px);\"><div style=\"padding:16px;\"> <a href=\"https:\/\/www.instagram.com\/p\/Cnyly08uA1_\/?utm_source=ig_embed&amp;utm_campaign=loading\" style=\" background:#FFFFFF; line-height:0; padding:0 0; text-align:center; text-decoration:none; width:100%;\" target=\"_blank\" rel=\"noopener\"> <div style=\" display: flex; flex-direction: row; align-items: center;\"> <div style=\"background-color: #F4F4F4; border-radius: 50%; flex-grow: 0; height: 40px; margin-right: 14px; width: 40px;\"><\/div> <div style=\"display: flex; flex-direction: column; flex-grow: 1; justify-content: center;\"> <div style=\" background-color: #F4F4F4; border-radius: 4px; flex-grow: 0; height: 14px; margin-bottom: 6px; width: 100px;\"><\/div> <div style=\" background-color: #F4F4F4; border-radius: 4px; flex-grow: 0; height: 14px; width: 60px;\"><\/div><\/div><\/div><div style=\"padding: 19% 0;\"><\/div> <div style=\"display:block; height:50px; margin:0 auto 12px; width:50px;\"><svg width=\"50px\" height=\"50px\" viewBox=\"0 0 60 60\" version=\"1.1\" xmlns=\"https:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"https:\/\/www.w3.org\/1999\/xlink\"><g stroke=\"none\" stroke-width=\"1\" fill=\"none\" fill-rule=\"evenodd\"><g transform=\"translate(-511.000000, -20.000000)\" fill=\"#000000\"><g><path d=\"M556.869,30.41 C554.814,30.41 553.148,32.076 553.148,34.131 C553.148,36.186 554.814,37.852 556.869,37.852 C558.924,37.852 560.59,36.186 560.59,34.131 C560.59,32.076 558.924,30.41 556.869,30.41 M541,60.657 C535.114,60.657 530.342,55.887 530.342,50 C530.342,44.114 535.114,39.342 541,39.342 C546.887,39.342 551.658,44.114 551.658,50 C551.658,55.887 546.887,60.657 541,60.657 M541,33.886 C532.1,33.886 524.886,41.1 524.886,50 C524.886,58.899 532.1,66.113 541,66.113 C549.9,66.113 557.115,58.899 557.115,50 C557.115,41.1 549.9,33.886 541,33.886 M565.378,62.101 C565.244,65.022 564.756,66.606 564.346,67.663 C563.803,69.06 563.154,70.057 562.106,71.106 C561.058,72.155 560.06,72.803 558.662,73.347 C557.607,73.757 556.021,74.244 553.102,74.378 C549.944,74.521 548.997,74.552 541,74.552 C533.003,74.552 532.056,74.521 528.898,74.378 C525.979,74.244 524.393,73.757 523.338,73.347 C521.94,72.803 520.942,72.155 519.894,71.106 C518.846,70.057 518.197,69.06 517.654,67.663 C517.244,66.606 516.755,65.022 516.623,62.101 C516.479,58.943 516.448,57.996 516.448,50 C516.448,42.003 516.479,41.056 516.623,37.899 C516.755,34.978 517.244,33.391 517.654,32.338 C518.197,30.938 518.846,29.942 519.894,28.894 C520.942,27.846 521.94,27.196 523.338,26.654 C524.393,26.244 525.979,25.756 528.898,25.623 C532.057,25.479 533.004,25.448 541,25.448 C548.997,25.448 549.943,25.479 553.102,25.623 C556.021,25.756 557.607,26.244 558.662,26.654 C560.06,27.196 561.058,27.846 562.106,28.894 C563.154,29.942 563.803,30.938 564.346,32.338 C564.756,33.391 565.244,34.978 565.378,37.899 C565.522,41.056 565.552,42.003 565.552,50 C565.552,57.996 565.522,58.943 565.378,62.101 M570.82,37.631 C570.674,34.438 570.167,32.258 569.425,30.349 C568.659,28.377 567.633,26.702 565.965,25.035 C564.297,23.368 562.623,22.342 560.652,21.575 C558.743,20.834 556.562,20.326 553.369,20.18 C550.169,20.033 549.148,20 541,20 C532.853,20 531.831,20.033 528.631,20.18 C525.438,20.326 523.257,20.834 521.349,21.575 C519.376,22.342 517.703,23.368 516.035,25.035 C514.368,26.702 513.342,28.377 512.574,30.349 C511.834,32.258 511.326,34.438 511.181,37.631 C511.035,40.831 511,41.851 511,50 C511,58.147 511.035,59.17 511.181,62.369 C511.326,65.562 511.834,67.743 512.574,69.651 C513.342,71.625 514.368,73.296 516.035,74.965 C517.703,76.634 519.376,77.658 521.349,78.425 C523.257,79.167 525.438,79.673 528.631,79.82 C531.831,79.965 532.853,80.001 541,80.001 C549.148,80.001 550.169,79.965 553.369,79.82 C556.562,79.673 558.743,79.167 560.652,78.425 C562.623,77.658 564.297,76.634 565.965,74.965 C567.633,73.296 568.659,71.625 569.425,69.651 C570.167,67.743 570.674,65.562 570.82,62.369 C570.966,59.17 571,58.147 571,50 C571,41.851 570.966,40.831 570.82,37.631\"><\/path><\/g><\/g><\/g><\/svg><\/div><div style=\"padding-top: 8px;\"> <div style=\" color:#3897f0; font-family:Arial,sans-serif; font-size:14px; font-style:normal; font-weight:550; line-height:18px;\">View this post on Instagram<\/div><\/div><div style=\"padding: 12.5% 0;\"><\/div> <div style=\"display: flex; flex-direction: row; margin-bottom: 14px; align-items: center;\"><div> <div style=\"background-color: #F4F4F4; border-radius: 50%; height: 12.5px; width: 12.5px; transform: translateX(0px) translateY(7px);\"><\/div> <div style=\"background-color: #F4F4F4; height: 12.5px; transform: rotate(-45deg) translateX(3px) translateY(1px); width: 12.5px; flex-grow: 0; margin-right: 14px; margin-left: 2px;\"><\/div> <div style=\"background-color: #F4F4F4; border-radius: 50%; height: 12.5px; width: 12.5px; transform: translateX(9px) translateY(-18px);\"><\/div><\/div><div style=\"margin-left: 8px;\"> <div style=\" background-color: #F4F4F4; border-radius: 50%; flex-grow: 0; height: 20px; width: 20px;\"><\/div> <div style=\" width: 0; height: 0; border-top: 2px solid transparent; border-left: 6px solid #f4f4f4; border-bottom: 2px solid transparent; transform: translateX(16px) translateY(-4px) rotate(30deg)\"><\/div><\/div><div style=\"margin-left: auto;\"> <div style=\" width: 0px; border-top: 8px solid #F4F4F4; border-right: 8px solid transparent; transform: translateY(16px);\"><\/div> <div style=\" background-color: #F4F4F4; flex-grow: 0; height: 12px; width: 16px; transform: translateY(-4px);\"><\/div> <div style=\" width: 0; height: 0; border-top: 8px solid #F4F4F4; border-left: 8px solid transparent; transform: translateY(-4px) translateX(8px);\"><\/div><\/div><\/div> <div style=\"display: flex; flex-direction: column; flex-grow: 1; justify-content: center; margin-bottom: 24px;\"> <div style=\" background-color: #F4F4F4; border-radius: 4px; flex-grow: 0; height: 14px; margin-bottom: 6px; width: 224px;\"><\/div> <div style=\" background-color: #F4F4F4; border-radius: 4px; flex-grow: 0; height: 14px; width: 144px;\"><\/div><\/div><\/a><p style=\" color:#c9c8cd; font-family:Arial,sans-serif; font-size:14px; line-height:17px; margin-bottom:0; margin-top:8px; overflow:hidden; padding:8px 0 7px; text-align:center; text-overflow:ellipsis; white-space:nowrap;\"><a href=\"https:\/\/www.instagram.com\/p\/Cnyly08uA1_\/?utm_source=ig_embed&amp;utm_campaign=loading\" style=\" color:#c9c8cd; font-family:Arial,sans-serif; font-size:14px; font-style:normal; font-weight:normal; line-height:17px; text-decoration:none;\" target=\"_blank\" rel=\"noopener\">A post shared by bgd peco (@barbe_generative_diary)<\/a><\/p><\/div><\/blockquote> <script async src=\"\/\/www.instagram.com\/embed.js\"><\/script>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TheStrangeAttractors-2\">Sample Code for openFrameworks<\/h2>\n\n\n\n<p>The sample code uses openFrameworks, but these Attractor formulas can also be used with other tools such as Processing.<\/p>\n\n\n\n<pre><code class=\"language-cpp\">\n#pragma once\n#include \"ofMain.h\"\n\nclass ofApp : public ofBaseApp{\n\n\tpublic:\n\t\tvoid setup() override;\n\t\tvoid update() override;\n\t\tvoid draw() override;\n\t\tvoid exit() override;\n\n\t\tvoid keyPressed(int key) override;\n\t\tvoid keyReleased(int key) override;\n\t\tvoid mouseMoved(int x, int y ) override;\n\t\tvoid mouseDragged(int x, int y, int button) override;\n\t\tvoid mousePressed(int x, int y, int button) override;\n\t\tvoid mouseReleased(int x, int y, int button) override;\n\t\tvoid mouseScrolled(int x, int y, float scrollX, float scrollY) override;\n\t\tvoid mouseEntered(int x, int y) override;\n\t\tvoid mouseExited(int x, int y) override;\n\t\tvoid windowResized(int w, int h) override;\n\t\tvoid dragEvent(ofDragInfo dragInfo) override;\n\t\tvoid gotMessage(ofMessage msg) override;\n\n    \/\/Attractors\n    void aizawaAtt();\n    void chuaAtt();\n    void halvorsenAtt();\n    void lorenzAtt();\n    void newtonLeipnikAtt();\n\n    float x, y, z;\n\n    float alpha;   \/\/ \u03b1\n    float beta;    \/\/ \u03b2\n    float camma;   \/\/ \u03b3\n    float delta;   \/\/ \u03b4\n    float epsilon; \/\/ \u03b5\n    float zehta;   \/\/ \u03b6\n    float rho;     \/\/ \u03c1\n    float Gx;\n\n    float dt;      \/\/ time\n    float scale;\n\n    vector<glm::vec3> pos;\n\n\/\/    ofEasyCam camera;\n};\n<\/code><\/pre>\n\n\n\n<pre><code class=\"language-cpp\">\n#include \"ofApp.h\"\n\n\/\/--------------------------------------------------------------\nvoid ofApp::setup(){\n    ofBackground(0);\n\n    x = 0.01;\n    y = 0;\n    z = 0;\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::update(){\n\n    pos.push_back(glm::vec3(x, y, z));\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::draw(){\n\n\/\/    camera.begin();\n    ofTranslate(ofGetWidth()\/2, ofGetHeight()\/2);\n\n\/\/Attractors\n    aizawaAtt();\n\/\/    chuaAtt();\n\/\/    halvorsenAtt();\n\/\/    lorenzAtt();\n\/\/    newtonLeipnikAtt();\n\n    update();\n\n    ofSetColor(255);\n    ofNoFill();\n    ofBeginShape();\n    for(glm::vec3 v : pos){\n        ofVertex(v.x * scale, v.y * scale, v.z * scale);\n    }\n    ofEndShape();\n\/\/    camera.end();\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::aizawaAtt(){\n\n    alpha = 0.95;   \/\/ \u03b1\n    beta = 0.7;     \/\/ \u03b2\n    camma = 0.6;    \/\/ \u03b3\n    delta = 3.5;    \/\/ \u03b4\n    epsilon = 0.25; \/\/ \u03b5\n    zehta = 0.1;      \/\/ \u03c1\n\n    scale = 150.0;\n    dt = 0.01;\n    float dx = (z - beta) * x - delta * y;\n    float dy = delta * x + (z - beta) * y;\n    float dz = camma + alpha * z  - pow(z,3) \/ 3 - (pow(x,2) + pow(y,2)) * (1 + epsilon * z) + zehta * z * pow(x,3);\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::chuaAtt(){\n\n    alpha = 15.6;   \/\/ \u03b1\n    beta = 1.0;     \/\/ \u03b2\n    camma = 25.58;  \/\/ \u03b3\n    delta = -1;     \/\/ \u03b4\n    epsilon = 0;    \/\/ \u03b5\n\n    Gx = epsilon*x + (delta + epsilon) * (abs(x + 1) - abs(x - 1));\n\n    scale = 60.0;\n    dt = 0.01;\n\n    float dx = alpha * (y - x - Gx);\n    float dy = beta * (x - y + z);\n    float dz = -(camma * y);\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::halvorsenAtt(){\n\n    alpha = 1.4;   \/\/ \u03b1\n\n    scale = 25.0;\n    dt = 0.005;\n    float dx = -alpha*x -4*y -4*z - y*y;\n    float dy = -alpha*y -4*z -4*x - z*z;\n    float dz = -alpha*z -4*x -4*y - x*x;\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::lorenzAtt(){\n\n    beta = 8.0\/3.0;   \/\/ \u03b2\n    delta = 10;       \/\/ \u03b4\n    rho = 28;         \/\/ \u03c1\n\n    scale = 7.0;\n    dt = 0.01;\n    float dx = (delta * (y - x));\n    float dy = (x * (rho - z) - y);\n    float dz = (x * y - beta * z);\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n\n\/\/--------------------------------------------------------------\nvoid ofApp::newtonLeipnikAtt(){\n\n    alpha = 0.4;    \/\/ \u03b1\n    beta = 0.175;   \/\/ \u03b2\n\n    scale = 300.0;\n    dt = 0.01;\n    float dx = -alpha * x + y + 10 * y * z;\n    float dy = -x - 0.4 * y + 5 * x * z;\n    float dz = beta * z - 5 * x * y;\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TheStrangeAttractors-3\">The Strange Attractors<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TheStrangeAttractors-3-1\">The Aizawa Attractor<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"576\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/01-TheAizawaAttractors.webp\" alt=\"\" class=\"wp-image-445 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/01-TheAizawaAttractors.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/01-TheAizawaAttractors-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/01-TheAizawaAttractors-768x432.webp 768w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/576;\" \/><\/figure>\n\n\n\n<p><strong>Equations:<\/strong><br>dx\/dt = (z &#8211; \u03b2)x &#8211; \u03b4y<br>dy\/dt = \u03b4x + (z &#8211; \u03b2)y<br>dz\/dt = \u03b3 + \u03b1z &#8211; pow(z,3) \/ 3 &#8211; (pow(x,2) + pow(y,2))(1 + \u03b5 * z) + \u03c1z pow(x,3)<\/p>\n\n\n\n<p><strong>Parameter: <\/strong><br>\u03b1 = 0.95<br>\u03b2 = 0.7<br>\u03b3 = 0.6<br>\u03b4 = 3.5<br>\u03b5 = 0.25<br>\u03c1 = 0.1<\/p>\n\n\n\n<p>dt = 0.01<\/p>\n\n\n\n<pre><code class=\"language-cpp\">\nvoid ofApp::aizawaAtt(){\n\n    alpha = 0.95;   \/\/ \u03b1\n    beta = 0.7;     \/\/ \u03b2\n    camma = 0.6;    \/\/ \u03b3\n    delta = 3.5;    \/\/ \u03b4\n    epsilon = 0.25; \/\/ \u03b5\n    zehta = 0.1;    \/\/ \u03c1\n\n    scale = 150.0;\n    dt = 0.01;\n    float dx = (z - beta) * x - delta * y;\n    float dy = delta * x + (z - beta) * y;\n    float dz = camma + alpha * z  - pow(z,3) \/ 3 - (pow(x,2) + pow(y,2)) * (1 + epsilon * z) + zehta * z * pow(x,3);\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"-TheStrangeAttractors-3-2\">The Chua Attractor<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"576\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/02-TheChuaAttractors.webp\" alt=\"\" class=\"wp-image-446 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/02-TheChuaAttractors.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/02-TheChuaAttractors-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/02-TheChuaAttractors-768x432.webp 768w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/576;\" \/><\/figure>\n\n\n\n<p><strong>Equations:<\/strong><br>dx\/dt = \u03b1(y &#8211; x &#8211; G(x))<br>dy\/dt = \u03b2(x &#8211; y + z)<br>dz\/dt = -\u03b3y<\/p>\n\n\n\n<p><strong>Parameter:<\/strong><br>\u03b1 = 15.6<br>\u03b2 = 1.0<br>\u03b3 = 25.58<br>\u03b4 = -1<br>\u03b5 = 0<\/p>\n\n\n\n<p>G(x) = \u03b5x + (\u03b4 + \u03b5)(abs(x + 1) &#8211; abs(x &#8211; 1))<br>dt = 0.01<\/p>\n\n\n\n<pre><code class=\"language-cpp\">\nvoid ofApp::chuaAtt(){\n\n    alpha = 15.6;   \/\/ \u03b1\n    beta = 1.0;     \/\/ \u03b2\n    camma = 25.58;  \/\/ \u03b3\n    delta = -1;     \/\/ \u03b4\n    epsilon = 0;    \/\/ \u03b5\n\n    Gx = epsilon*x + (delta + epsilon) * (abs(x + 1) - abs(x - 1));\n\n    scale = 60.0;\n    dt = 0.01;\n\n    float dx = alpha * (y - x - Gx);\n    float dy = beta * (x - y + z);\n    float dz = -(camma * y);\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TheStrangeAttractors-3-3\">The Halvorsen Attractor<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"576\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/03-TheHalvorsenAttractors.webp\" alt=\"\" class=\"wp-image-447 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/03-TheHalvorsenAttractors.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/03-TheHalvorsenAttractors-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/03-TheHalvorsenAttractors-768x432.webp 768w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/576;\" \/><\/figure>\n\n\n\n<p><strong>Equations:<\/strong><br>dx\/dt = -\u03b1x &#8211; 4y &#8211; 4z &#8211; yy<br>dy\/dt = -\u03b1y &#8211; 4z &#8211; 4x &#8211; zz<br>dz\/dt = -\u03b1z &#8211; 4x &#8211; 4y &#8211; xx<\/p>\n\n\n\n<p><strong>Parameter:<\/strong><br>\u03b1 = 1.4<br>dt = 0.005<\/p>\n\n\n\n<pre><code class=\"language-cpp\">\nvoid ofApp::halvorsenAtt(){\n\n    alpha = 1.4;   \/\/ \u03b1\n\n    scale = 25.0;\n    dt = 0.005;\n    float dx = -alpha*x -4*y -4*z - y*y;\n    float dy = -alpha*y -4*z -4*x - z*z;\n    float dz = -alpha*z -4*x -4*y - x*x;\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n\n<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TheStrangeAttractors-3-4\">The Lorenz Attractor<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"576\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/04-TheLorenzAttractors.webp\" alt=\"\" class=\"wp-image-448 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/04-TheLorenzAttractors.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/04-TheLorenzAttractors-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/04-TheLorenzAttractors-768x432.webp 768w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/576;\" \/><\/figure>\n\n\n\n<p><strong>Equations:<\/strong><br>dx\/dt = \u03b4(y &#8211; x)<br>dy\/dt  = x(\u03c1 &#8211; z) &#8211; y<br>dz\/dt  = xy &#8211; \u03b2z<\/p>\n\n\n\n<p><strong>Parameter:<\/strong><br>\u03b2 = 8.0\/3.0<br>\u03b4 = 10<br>\u03c1 = 28<\/p>\n\n\n\n<p>dt = 0.01<\/p>\n\n\n\n<pre><code class=\"language-cpp\">\nvoid ofApp::lorenzAtt(){\n\n    beta = 8.0\/3.0;   \/\/ \u03b2\n    delta = 10;       \/\/ \u03b4\n    rho = 28;         \/\/ \u03c1\n\n    scale = 7.0;\n    dt = 0.01;\n    float dx = (delta * (y - x));\n    float dy = (x * (rho - z) - y);\n    float dz = (x * y - beta * z);\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TheStrangeAttractors-3-5\">The Newton &#8211; Lepnik Attractor<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"576\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/05-TheNewtonLeipnikAttractors.webp\" alt=\"\" class=\"wp-image-449 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/05-TheNewtonLeipnikAttractors.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/05-TheNewtonLeipnikAttractors-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/01\/05-TheNewtonLeipnikAttractors-768x432.webp 768w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/576;\" \/><\/figure>\n\n\n\n<p><strong>Equations:<\/strong><br>dx\/dt = -\u03b1x + y + 10yz<br>dy\/dt = -x &#8211; 0.4y + 5xz<br>dz\/dt = \u03b2z &#8211; 5xy<\/p>\n\n\n\n<p><strong>Parameter: <\/strong><br>\u03b1 = 0.4<br>\u03b2 = 0.175<\/p>\n\n\n\n<p>dt = 0.01<\/p>\n\n\n\n<pre><code class=\"language-cpp\">\nvoid ofApp::newtonLeipnikAtt(){\n\n    alpha = 0.4;    \/\/ \u03b1\n    beta = 0.175;   \/\/ \u03b2\n\n    scale = 300.0;\n    dt = 0.01;\n    float dx = -alpha * x + y + 10 * y * z;\n    float dy = -x - 0.4 * y + 5 * x * z;\n    float dz = beta * z - 5 * x * y;\n    x = x + dx * dt;\n    y = y + dy * dt;\n    z = z + dz * dt;\n}\n<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Recommended Book \/ Generative art for beginner<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"576\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2023\/09\/GenerativeArtProcessing.webp\" alt=\"\" class=\"wp-image-327 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2023\/09\/GenerativeArtProcessing.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2023\/09\/GenerativeArtProcessing-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2023\/09\/GenerativeArtProcessing-768x432.webp 768w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/576;\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><a href=\"https:\/\/amzn.to\/3rBeaOZ\" target=\"_blank\" rel=\"noreferrer noopener\">Generative Art: A Practical Guide Using Processing<\/a><a href=\"https:\/\/amzn.to\/45Xzptl\" target=\"_blank\" rel=\"noreferrer noopener\">&nbsp;<\/a>\u2013 Matt Pearson<\/h3>\n\n\n\n<p>Generative Art presents both the techniques and the beauty of algorithmic art. In it, you\u2019ll find dozens of high-quality examples of generative art, along with the specific steps the author followed to create each unique piece using the Processing programming language. The book includes concise tutorials for each of the technical components required to create the book\u2019s images, and it offers countless suggestions for how you can combine and reuse the various techniques to create your own works.<\/p>\n\n\n\n<p>Purchase of the print book comes with an offer of a free PDF, ePub, and Kindle eBook from Manning. Also available is all code from the book.<br>\u2014\u2013<br>\u25ba&nbsp;<strong><a href=\"https:\/\/amzn.to\/3rBeaOZ\" target=\"_blank\" rel=\"noreferrer noopener\">Generative Art: A Practical Guide Using Processing<\/a><\/strong>&nbsp;\u2013 Matt Pearson<br>Publication date: 2011. July <\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Strange Attractor draws a chaotic and beautiful trajectory. Many code artists use it to create graphics using these code because these allow them to record trajectories (numerical values) in space over time.<\/p>\n","protected":false},"author":1,"featured_media":444,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,3,32,13],"tags":[],"class_list":["post-442","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-artworks","category-codeart","category-openframeworks-tutorials","category-tutorials"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts\/442","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/comments?post=442"}],"version-history":[{"count":3,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts\/442\/revisions"}],"predecessor-version":[{"id":451,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts\/442\/revisions\/451"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/media\/444"}],"wp:attachment":[{"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/media?parent=442"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/categories?post=442"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/tags?post=442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}