Problem 785. Mandelbrot Number Test [Real+Imaginary]

Created by Richard Zapor

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Mandelbrot_set\"><w:r><w:t>Mandelbrot Set</w:t></w:r></w:hyperlink><w:r><w:t> is built around a simple iterative equation.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ z(1)   = c\n z(n+1) = z(n)^2 + c]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Mandelbrot numbers remain bounded for n through infinity. These numbers have a real and complex component.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For a vector of real and complex components determine if each is a Mandelbrot number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If abs(z)&gt;2 then z will escape to infinity and is thus NOT valid.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Input:</w:t></w:r><w:r><w:t> [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Output:</w:t></w:r><w:r><w:t> [1 ; 0 ; 1 ; 0 ; 1 ; 1] ...Where 1 is for a Valid Mandelbrot</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Cleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\"><w:r><w:t>Chapter 10, Mandelbrot Set (PDF)</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Problem based upon</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\"><w:r><w:t>Cody 81: Mandelbrot Numbers</w:t></w:r></w:hyperlink></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

62 Solutions
19 Solvers

Last Solution submitted on May 22, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers19

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 785. Mandelbrot Number Test [Real+Imaginary]

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers19

Suggested Problems

More from this Author255

Problem Tags

Community Treasure Hunt

Problem 785. Mandelbrot Number Test [Real+Imaginary]

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers19

Suggested Problems

More from this Author255

Problem Tags

Community Treasure Hunt

Players