{"id":457,"date":"2024-03-13T10:33:24","date_gmt":"2024-03-13T01:33:24","guid":{"rendered":"https:\/\/barbegenerativediary.com\/en\/?p=457"},"modified":"2024-03-13T10:33:24","modified_gmt":"2024-03-13T01:33:24","slug":"how-to-create-minkowski-distance-circles-with-processing","status":"publish","type":"post","link":"https:\/\/barbegenerativediary.com\/en\/tutorials\/how-to-create-minkowski-distance-circles-with-processing\/","title":{"rendered":"How to create Minkowski Distance Circles with Processing."},"content":{"rendered":"\n<h3 class=\"wp-block-heading\"><strong>Index<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"#MinkowskiDistance-01\" title=\"\"><strong>Sample Graphic of barbe_generative_diary<\/strong><\/a><\/li>\n\n\n\n<li><strong><a href=\"#MinkowskiDistance-02\" title=\"\">What is Minkowski Distance?<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#MinkowskiDistance-03\" title=\"\">Understanding Different Orders of Minkowski Distance<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#MinkowskiDistance-04\" title=\"\">How to create a Minkowski Distance Circles with Processing<\/a><\/strong><\/li>\n\n\n\n<li><strong><a href=\"#MinkowskiDistance-05\" title=\"\">Recommended Book \/ Generative art for beginner<\/a><\/strong><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"MinkowskiDistance-01\">Sample Graphic of barbe_generative_diary<\/h2>\n\n\n\n<p>This is a barbe_generative_diary\u2019s graphic sample using Minkowski Distance.<\/p>\n\n\n\n<blockquote class=\"instagram-media\" data-instgrm-permalink=\"https:\/\/www.instagram.com\/reel\/DHTdWVNSBxL\/?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\/reel\/DHTdWVNSBxL\/?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\"> <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\/reel\/DHTdWVNSBxL\/?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\">A post shared by bgd peco (@barbe_generative_diary)<\/a><\/p><\/div><\/blockquote>\n<script async src=\"\/\/www.instagram.com\/embed.js\"><\/script>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"instagram-media\" data-instgrm-permalink=\"https:\/\/www.instagram.com\/reel\/C40dg0bSpwo\/?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\/reel\/C40dg0bSpwo\/?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\/reel\/C40dg0bSpwo\/?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>In the realm of data science and machine learning, metrics play a pivotal role in quantifying the similarity or dissimilarity between data points. One such metric that holds significant importance is the Minkowski distance. Named after the German mathematician Hermann Minkowski, this distance measure serves as a versatile tool in various fields, including pattern recognition, image processing, and clustering analysis. Let\u2019s delve deeper into what Minkowski distance entails and how it creates circles using Minkowski distance with program code.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"MinkowskiDistance-02\">What is Minkowski Distance?<\/h2>\n\n\n\n<p>Minkowski distance is a generalized metric that calculates the distance between two points in a multidimensional space. It is essentially a measure of dissimilarity between two vectors in a normed vector space. The formula for calculating the Minkowski distance between two points, <em><strong>X<\/strong><\/em> and <em><strong>Y<\/strong><\/em>, in an <em>n<\/em>-dimensional space is given by:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"288\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-01-1024x288.webp\" alt=\"\" class=\"wp-image-463 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-01-1024x288.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-01-300x84.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-01-768x216.webp 768w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-01.webp 1191w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/288;\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>D<\/em>(<em>X<\/em>,<em>Y<\/em>)<\/strong> represents the Minkowski distance between points <em><strong>X<\/strong><\/em> and <em><strong>Y<\/strong><\/em>.<\/li>\n\n\n\n<li><strong><em>xi<\/em>\u200b<\/strong> and <strong><em>yi<\/em>\u200b<\/strong> are the corresponding components of the two points in the <em><strong>i th<\/strong><\/em> dimension.<\/li>\n\n\n\n<li><em><strong>p<\/strong><\/em> is a parameter that defines the order of the Minkowski distance. When <em><strong>p<\/strong><\/em>=1, it corresponds to the <strong>Manhattan distance<\/strong>, and when <em><strong>p<\/strong><\/em>=2, it represents the <strong>Euclidean distance<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"MinkowskiDistance-03\">Understanding Different Orders of Minkowski Distance<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Manhattan Distance (<em>p<\/em>=1):<\/strong> Also known as city block distance or taxicab distance, the Manhattan distance calculates the distance between two points along the grid-like paths. It is computed as the sum of the absolute differences of their Cartesian coordinates.<\/li>\n\n\n\n<li><strong>Euclidean Distance (<em>p<\/em>=2):<\/strong> Perhaps the most familiar distance metric, the Euclidean distance represents the straight-line distance between two points in space. It is derived from the Pythagorean theorem and measures the length of the line segment connecting the two points.<\/li>\n\n\n\n<li><strong>Other Orders:<\/strong> Minkowski distance isn&#8217;t restricted to just <em>p<\/em>=1 and <em><em>p<\/em><\/em>=2. It can accommodate any real number <em>p<\/em>\u22651. Higher values of <em>p<\/em> give more weight to large differences in one dimension, whereas lower values spread the weight more evenly.<\/li>\n<\/ol>\n\n\n\n<p>The following figure shows unit circles (the level set of the distance function where all points are at the unit distance from the center) with various values of <em><strong>p<\/strong><\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"288\" data-src=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-02-1024x288.webp\" alt=\"\" class=\"wp-image-464 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-02-1024x288.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-02-300x84.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-02-768x216.webp 768w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-02.webp 1191w\" data-sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 1024px; --smush-placeholder-aspect-ratio: 1024\/288;\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"MinkowskiDistance-04\">How to create a Minkowski Distance Circles with Processing<\/h2>\n\n\n\n<p>The code below is created separately for each HALF_PI.<\/p>\n\n\n\n<pre><code class=\"language-processing\">\n\/\/Minkowski distance|Circles\nfloat radius = 200;\nvoid setup() {\n  size(500, 500);\n  noFill();\n}\n\nvoid draw() {\n  background(255);\n  translate(width \/ 2, height \/ 2);\n  \n  noStroke();\n  fill(0,100);\n  minkowskiCircles();\n}\n\nvoid minkowskiCircles() {\n  float[] pValues = {0.5, 1, 2, 3};\n  for (float p : pValues) {\n    beginShape();\n    for(int i=0; i<4; i++){\n      for (float angle = 0; angle < HALF_PI; angle += 0.01) {\n        float x = cos(angle + HALF_PI*i);\n        float y = sin(angle + HALF_PI*i);\n        float scale = pow(pow(abs(x), p) + pow(abs(y), p), 1\/p);\n        vertex(radius * x \/ scale, radius * y \/ scale);\n      }\n    }\n    endShape(CLOSE);\n  }\n}\n<\/code><\/pre>\n\n\n\n<p>Result:<\/p>\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\/03\/minkowski-03.webp\" alt=\"\" class=\"wp-image-466 lazyload\" data-srcset=\"https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-03.webp 1024w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-03-300x169.webp 300w, https:\/\/barbegenerativediary.com\/en\/wp-content\/uploads\/2024\/03\/minkowski-03-768x432.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><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"MinkowskiDistance-05\">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>This article describes how to create shapes (circles) using Minkowski distance with Processing.<\/p>\n","protected":false},"author":1,"featured_media":473,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,13],"tags":[],"class_list":["post-457","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-processing-tutorials","category-tutorials"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts\/457","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=457"}],"version-history":[{"count":16,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"predecessor-version":[{"id":649,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/posts\/457\/revisions\/649"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/media\/473"}],"wp:attachment":[{"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/barbegenerativediary.com\/en\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}