{"id":3476,"date":"2018-06-25T12:00:38","date_gmt":"2018-06-25T17:00:38","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=3476"},"modified":"2018-11-24T12:22:35","modified_gmt":"2018-11-24T17:22:35","slug":"greg-searle-fractal-art-and-design","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2018\/06\/25\/greg-searle-fractal-art-and-design\/","title":{"rendered":"Greg Searle, Fractal Art and Design"},"content":{"rendered":"<div class=\"content\"><!--introduction--><p>If you follow this blog regularly, you know that I love fractals. I recently spent a pleasant afternoon in Nashua, New Hampshire, where my daughter Teresa introduced me to Gregory Searle, a fractal artist and computer geek.  Here is his logo.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/greg_logo.jpg\" alt=\"\"> <\/p><!--\/introduction--><h3>Contents<\/h3><div><ul><li><a href=\"#91273a32-8ea2-48a2-a4a1-f4a0ac1ed22d\">Fractal Generator<\/a><\/li><li><a href=\"#178efeee-a059-4769-a704-24062c129da5\">Double Double<\/a><\/li><li><a href=\"#5505c6f5-9538-47c1-a23b-9b217bedac8b\">Aquifer<\/a><\/li><li><a href=\"#8bf8dfec-073e-41fa-aa5d-9c1999f6924c\">Amphibian<\/a><\/li><li><a href=\"#2d4c4fb6-4dbe-4497-921d-3930e7eb285d\">Clematis<\/a><\/li><li><a href=\"#8910a435-f78d-4515-a3a9-3a48f2dffcb6\">Wavelets<\/a><\/li><li><a href=\"#513feaa1-ba71-4d8d-b143-d091fd24313c\">Mandelbar<\/a><\/li><li><a href=\"#cdffcd69-2e50-4761-bc1b-687cd8fb958f\">Burning Ship<\/a><\/li><\/ul><\/div><h4>Fractal Generator<a name=\"91273a32-8ea2-48a2-a4a1-f4a0ac1ed22d\"><\/a><\/h4><p>Greg's web page is <a href=\"http:\/\/www.fractalartdesign.com\">&lt;http:\/\/www.fractalartdesign.com<\/a>&gt;.  There is much to explore. To get started, click on \"Fractal Generator\" in the menu on the left of the page, and then on the \"Fractal Generator\" icon in the center of the next page.  Or go directly to <a href=\"http:\/\/fractal.fractalartdesign.com\">&lt;http:\/\/fractal.fractalartdesign.com<\/a>&gt;.<\/p><p>You will find yourself in an app, written in JavaScript and running in your browser, where you can endlessly explore the Mandelbrot set and an unlimited collection of variations.  You can zoom, pan, change iterators, vary parameters, and select from almost two dozen themes or color maps. You can edit the colormaps and investigate smoothers, renderers, and other effects.<\/p><p>This is the tool that Greg uses to produce his art.  He writes, \"A painter uses paints; I use a CPU. I am giving you access to my paints! Please be aware that this is always a work in progress. It will change at a whim.\"<\/p><p>There is a lot of fractal art on the Web.  This tool allows you to create your own.<\/p><h4>Double Double<a name=\"178efeee-a059-4769-a704-24062c129da5\"><\/a><\/h4><p>Zooming in on a Mandelbrot or similar fractal by a factor approaching $2^{53}$ reaches the limit of IEEE double precision floating point. So, Greg's generator switches to <i>double double<\/i> precision. This doubles the fraction length and slows the rendering significantly. It does not increase the exponent, but these calculations need more precision, not more range.  (See <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2017\/05\/22\/quadruple-precision-128-bit-floating-point-arithmetic\">https:\/\/blogs.mathworks.com\/cleve\/2017\/05\/22\/quadruple-precision-128-bit-floating-point-arithmetic<\/a>.)<\/p><h4>Aquifer<a name=\"5505c6f5-9538-47c1-a23b-9b217bedac8b\"><\/a><\/h4><p>Greg uses his generator, and his skill, to create unique single-edition prints.  To preserve their value, he does not reveal the parameters and never reprints.  He displays his work at galleries and exhibitions around New England.  Some of it is shown, and offered for sale, on his web site.<\/p><p>Here is a sample.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/aquifer.jpg\" alt=\"\"> <\/p><p><i>Aquifer<\/i><\/p><h4>Amphibian<a name=\"8bf8dfec-073e-41fa-aa5d-9c1999f6924c\"><\/a><\/h4><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/amphibian.jpg\" alt=\"\"> <\/p><p><i>Amphibian<\/i><\/p><h4>Clematis<a name=\"2d4c4fb6-4dbe-4497-921d-3930e7eb285d\"><\/a><\/h4><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/clematis.jpg\" alt=\"\"> <\/p><p><i>Clematis<\/i><\/p><h4>Wavelets<a name=\"8910a435-f78d-4515-a3a9-3a48f2dffcb6\"><\/a><\/h4><p>Here is one of his wallpapers, digital images that are available as a free download for use as a desktop background or device lock screen.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/wavelets.jpg\" alt=\"\"> <\/p><p><i>Wavelets<\/i><\/p><h4>Mandelbar<a name=\"513feaa1-ba71-4d8d-b143-d091fd24313c\"><\/a><\/h4><p>Greg did not make the next two images -- I did, using his generator and nonstandard iterators.  The color themes and shading are novel. This one is known on the Internet as the \"Mandelbar\" set because the iterator uses the complex conjugate, with a bar over the $z$,<\/p><p>$$z = \\bar{z}^2 + c$$<\/p><p>instead of the traditional<\/p><p>$$z = z^2 + c$$<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/mandelbar.png\" alt=\"\"> <\/p><p><i>Mandelbar<\/i><\/p><h4>Burning Ship<a name=\"cdffcd69-2e50-4761-bc1b-687cd8fb958f\"><\/a><\/h4><p>And this amazing fractal, known as the \"Burning Ship\", is produced by zooming in on an iterator involving the complex absolute value.<\/p><p>$$z = |z|^2 + c$$<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/ship.png\" alt=\"\"> <\/p><p><i>Burning Ship<\/i><\/p><p>To see much more of the Burning Ship fractal, check out this video, <a href=\"https:\/\/www.youtube.com\/watch?v=CD9yNFmb2FE\">https:\/\/www.youtube.com\/watch?v=CD9yNFmb2FE<\/a>.<\/p><script language=\"JavaScript\"> <!-- \r\n    function grabCode_ffbd6f941824499bb2eb809dda7120f0() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='ffbd6f941824499bb2eb809dda7120f0 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' ffbd6f941824499bb2eb809dda7120f0';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2018 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_ffbd6f941824499bb2eb809dda7120f0()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; R2018a<br><\/p><\/div><!--\r\nffbd6f941824499bb2eb809dda7120f0 ##### SOURCE BEGIN #####\r\n%% Greg Searle, Fractal Art and Design\r\n% If you follow this blog regularly, you know that I love fractals.\r\n% I recently spent a pleasant afternoon in Nashua, New Hampshire, where\r\n% my daughter Teresa introduced me to Gregory Searle, a fractal artist\r\n% and computer geek.  Here is his logo.\r\n%\r\n% <<greg_logo.jpg>>\r\n\r\n%% Fractal Generator\r\n% Greg's web page is <http:\/\/www.fractalartdesign.com\r\n% http:\/\/www.fractalartdesign.com>.  There is much to explore.\r\n% To get started, click on \"Fractal Generator\" in the menu on the left\r\n% of the page, and then on the \"Fractal Generator\" icon in the center of\r\n% the next page.  Or go directly to <http:\/\/fractal.fractalartdesign.com\r\n% http:\/\/fractal.fractalartdesign.com>.\r\n\r\n%%\r\n% You will find yourself in an app, written in JavaScript and running\r\n% in your browser, where you can endlessly explore the Mandelbrot set\r\n% and an unlimited collection of variations.  You can zoom, pan, change\r\n% iterators, vary parameters, and select from almost two dozen themes or\r\n% color maps. You can edit the colormaps and investigate smoothers,\r\n% renderers, and other effects.\r\n\r\n%%\r\n% This is the tool that Greg uses to produce his art.  He writes,\r\n% \"A painter uses paints; I use a CPU. I am giving you access to my\r\n% paints! Please be aware that this is always a work in progress. \r\n% It will change at a whim.\"\r\n\r\n%%\r\n% There is a lot of fractal art on the Web.  This tool allows you to\r\n% create your own.\r\n\r\n%% Double Double\r\n% Zooming in on a Mandelbrot or similar fractal by a factor approaching\r\n% $2^{53}$ reaches the limit of IEEE double precision floating point.\r\n% So, Greg's generator switches to _double double_ precision.\r\n% This doubles the fraction length and slows the rendering significantly.\r\n% It does not increase the exponent, but these calculations need more\r\n% precision, not more range.  (See \r\n% <https:\/\/blogs.mathworks.com\/cleve\/2017\/05\/22\/quadruple-precision-128-bit-floating-point-arithmetic.>)\r\n\r\n%% Aquifer\r\n% Greg uses his generator, and his skill, to create unique single-edition\r\n% prints.  To preserve their value, he does not reveal the parameters\r\n% and never reprints.  He displays his work at galleries and exhibitions\r\n% around New England.  Some of it is shown, and offered for sale, on his\r\n% web site.\r\n%\r\n% Here is a sample.\r\n%\r\n% <<aquifer.jpg>>\r\n%\r\n% _Aquifer_\r\n\r\n%% Amphibian\r\n% <<amphibian.jpg>>\r\n%\r\n% _Amphibian_\r\n\r\n%% Clematis\r\n% <<clematis.jpg>>\r\n%\r\n% _Clematis_\r\n\r\n%% Wavelets\r\n% Here is one of his wallpapers, digital images that are available as a\r\n% free download for use as a desktop background or device lock screen.\r\n%\r\n% <<wavelets.jpg>>\r\n%\r\n% _Wavelets_\r\n\r\n%% Mandelbar\r\n% Greg did not make the next two images REPLACE_WITH_DASH_DASH I did, using his generator\r\n% and nonstandard iterators.  The color themes and shading are novel.\r\n% This one is known on the Internet as the \"Mandelbar\" set\r\n% because the iterator uses the complex conjugate, with a bar over the $z$,\r\n%\r\n% $$z = \\bar{z}^2 + c$$\r\n%\r\n% instead of the traditional\r\n%\r\n% $$z = z^2 + c$$\r\n%\r\n% <<mandelbar.png>>\r\n%\r\n% _Mandelbar_\r\n\r\n%% Burning Ship\r\n% And this amazing fractal, known as the \"Burning Ship\", is produced by\r\n% zooming in on an iterator involving the complex absolute value.\r\n%\r\n% $$z = |z|^2 + c$$\r\n%\r\n%\r\n% <<ship.png>>\r\n%\r\n% _Burning Ship_\r\n%\r\n%\r\n% To see much more of the Burning Ship fractal, check out this video,\r\n% <https:\/\/www.youtube.com\/watch?v=CD9yNFmb2FE>.\r\n##### SOURCE END ##### ffbd6f941824499bb2eb809dda7120f0\r\n-->","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/greg_logo.jpg\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div><!--introduction--><p>If you follow this blog regularly, you know that I love fractals. I recently spent a pleasant afternoon in Nashua, New Hampshire, where my daughter Teresa introduced me to Gregory Searle, a fractal artist and computer geek.  Here is his logo.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2018\/06\/25\/greg-searle-fractal-art-and-design\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":3496,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[32,18,5,23,8,7],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/3476"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=3476"}],"version-history":[{"count":2,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/3476\/revisions"}],"predecessor-version":[{"id":4176,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/3476\/revisions\/4176"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media\/3496"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=3476"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=3476"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=3476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}