[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki8\/burning-ship-fractal-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki8\/burning-ship-fractal-wikipedia\/","headline":"Burning Ship fractal – Wikipedia","name":"Burning Ship fractal – Wikipedia","description":"before-content-x4 From Wikipedia, the free encyclopedia after-content-x4 Complex plane fractal after-content-x4 High-quality overview image of the Burning Ship fractal High-quality","datePublished":"2015-02-18","dateModified":"2015-02-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki8\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki8\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d5\/Burning_Ship_20210818.png\/220px-Burning_Ship_20210818.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d5\/Burning_Ship_20210818.png\/220px-Burning_Ship_20210818.png","height":"124","width":"220"},"url":"https:\/\/wiki.edu.vn\/en\/wiki8\/burning-ship-fractal-wikipedia\/","wordCount":2375,"articleBody":" (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4From Wikipedia, the free encyclopedia (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Complex plane fractal (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4High-quality overview image of the Burning Ship fractal High-quality image of the large ship in the left antennaThe Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. R\u00f6ssler in 1992, is generated by iterating the function:zn+1=(|Re\u2061(zn)|+i|Im\u2061(zn)|)2+c,z0=0{displaystyle z_{n+1}=(|operatorname {Re} left(z_{n}right)|+i|operatorname {Im} left(z_{n}right)|)^{2}+c,quad z_{0}=0}in the complex plane (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4C{displaystyle mathbb {C} } which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy\u2013Riemann equations.[1]div{display:table-cell;padding:0.2em 0 0.6em 1.6em;text-align:center;font-weight:bold}.mw-parser-output .mod-gallery .main>div{display:table-cell}.mw-parser-output .mod-gallery .gallery{line-height:1.35em}.mw-parser-output .mod-gallery .footer>div{display:table-cell;padding:0.2em 0 0.6em 1.6em;text-align:right;font-size:80%;line-height:1em}.mw-parser-output .mod-gallery .title>div *,.mw-parser-output .mod-gallery .footer>div *{overflow:visible}.mw-parser-output .mod-gallery .gallerybox img{background:none!important}.mw-parser-output .mod-gallery .bordered-images .thumb img{border:solid #eaecf0 1px}.mw-parser-output .mod-gallery .whitebg .thumb{background:#fff!important}]]>Burning Ship fractal renderingsImplementation[edit] Animation of a continuous zoom-out to show the amount of detail for an implementation with 64 maximum iterationsThe below pseudocode implementation hardcodes the complex operations for Z. Consider implementing complex number operations to allow for more dynamic and reusable code. Note that the typical images of the Burning Ship fractal display the ship upright: the actual fractal, and that produced by the below pseudocode, is inverted along the x-axis.for each pixel (x, y) on the screen, do: x\u00a0:= scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.5, 1)) y\u00a0:= scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1, 1)) zx\u00a0:= x \/\/ zx represents the real part of z zy\u00a0:= y \/\/ zy represents the imaginary part of z iteration\u00a0:= 0 max_iteration\u00a0:= 100 while (zx*zx + zy*zy < 4 and iteration < max_iteration) do xtemp\u00a0:= zx*zx - zy*zy + x zy\u00a0:= abs(2*zx*zy) + y \/\/ abs returns the absolute value zx\u00a0:= xtemp iteration\u00a0:= iteration + 1 if iteration = max_iteration then \/\/ Belongs to the set return insideColor return (max_iteration \/ iteration) \u00d7 colorReferences[edit]^ Michael Michelitsch and Otto E. R\u00f6ssler (1992). “The “Burning Ship” and Its Quasi-Julia Sets”. In: Computers & Graphics Vol. 16, No. 4, pp. 435\u2013438, 1992. Reprinted in Clifford A. Pickover Ed. (1998). Chaos and Fractals: A Computer Graphical Journey \u2014 A 10 Year Compilation of Advanced Research. Amsterdam, Netherlands: Elsevier.ISBN\u00a00-444-50002-2External links[edit]li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:\" \"counter(listitem)\"a0 \"}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:\" (\"counter(listitem)\"a0 \"}]]>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}]]> (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki8\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki8\/burning-ship-fractal-wikipedia\/#breadcrumbitem","name":"Burning Ship fractal – Wikipedia"}}]}]