{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":785,"title":"Mandelbrot Number Test [Real+Imaginary]","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\r\n\r\nFor a vector of real and complex components determine if each is a Mandelbrot number.\r\n\r\nIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\r\n\r\n*Input:* [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\r\n\r\n*Output:* [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf Chapter 10, Mandelbrot Set (PDF)\u003e\r\n\r\nProblem based upon \u003chttp://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers Cody 81: Mandelbrot Numbers\u003e","description_html":"\u003cp\u003eThe \u003ca href=\"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003eMandelbrot Set\u003c/a\u003e is built around a simple iterative equation.\u003c/p\u003e\u003cpre\u003e z(1)   = c\r\n z(n+1) = z(n)^2 + c\u003c/pre\u003e\u003cp\u003eMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\u003c/p\u003e\u003cp\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/p\u003e\u003cp\u003eIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\u003c/p\u003e\u003cp\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003ca href=\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\"\u003eChapter 10, Mandelbrot Set (PDF)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eProblem based upon \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\"\u003eCody 81: Mandelbrot Numbers\u003c/a\u003e\u003c/p\u003e","function_template":"function tf = isMandelbrot(v)\r\n  tf=abs(v)\u003c=2;\r\nend","test_suite":"%%\r\nformat long\r\n\r\nv=[-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25];\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 0 ; 1 ; 0 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=-.25*ones(6,1)+(rand(6,1)-.5)/2+i*(rand(6,1)-.5)/2\r\n\r\n%v=[-.5-.25i;-.5+.25i;-.25i;.25i;-.25-.25i;-.25+.25i]\r\n% Bounding Cases\r\n\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 1 ; 1 ; 1 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=rand(6,1)-0.25\r\ntf=isMandelbrot(v);\r\n\r\ntf_expected=v\u003c=0.25; % non-imaginary range [-2.0,0.25]\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',v,tf,tf_expected))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-22T13:35:21.000Z","updated_at":"2026-03-04T14:19:08.000Z","published_at":"2012-07-05T03:42:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot numbers remain bounded for n through infinity. These numbers have a real and complex component.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf abs(z)\u0026gt;2 then z will escape to infinity and is thus NOT valid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1] ...Where 1 is for a Valid Mandelbrot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChapter 10, Mandelbrot Set (PDF)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem based upon\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 81: Mandelbrot Numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":785,"title":"Mandelbrot Number Test [Real+Imaginary]","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\r\n\r\nFor a vector of real and complex components determine if each is a Mandelbrot number.\r\n\r\nIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\r\n\r\n*Input:* [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\r\n\r\n*Output:* [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf Chapter 10, Mandelbrot Set (PDF)\u003e\r\n\r\nProblem based upon \u003chttp://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers Cody 81: Mandelbrot Numbers\u003e","description_html":"\u003cp\u003eThe \u003ca href=\"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003eMandelbrot Set\u003c/a\u003e is built around a simple iterative equation.\u003c/p\u003e\u003cpre\u003e z(1)   = c\r\n z(n+1) = z(n)^2 + c\u003c/pre\u003e\u003cp\u003eMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\u003c/p\u003e\u003cp\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/p\u003e\u003cp\u003eIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\u003c/p\u003e\u003cp\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003ca href=\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\"\u003eChapter 10, Mandelbrot Set (PDF)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eProblem based upon \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\"\u003eCody 81: Mandelbrot Numbers\u003c/a\u003e\u003c/p\u003e","function_template":"function tf = isMandelbrot(v)\r\n  tf=abs(v)\u003c=2;\r\nend","test_suite":"%%\r\nformat long\r\n\r\nv=[-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25];\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 0 ; 1 ; 0 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=-.25*ones(6,1)+(rand(6,1)-.5)/2+i*(rand(6,1)-.5)/2\r\n\r\n%v=[-.5-.25i;-.5+.25i;-.25i;.25i;-.25-.25i;-.25+.25i]\r\n% Bounding Cases\r\n\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 1 ; 1 ; 1 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=rand(6,1)-0.25\r\ntf=isMandelbrot(v);\r\n\r\ntf_expected=v\u003c=0.25; % non-imaginary range [-2.0,0.25]\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',v,tf,tf_expected))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-22T13:35:21.000Z","updated_at":"2026-03-04T14:19:08.000Z","published_at":"2012-07-05T03:42:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot numbers remain bounded for n through infinity. These numbers have a real and complex component.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf abs(z)\u0026gt;2 then z will escape to infinity and is thus NOT valid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1] ...Where 1 is for a Valid Mandelbrot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChapter 10, Mandelbrot Set (PDF)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem based 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