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In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions.〔()〕 As a result, it is an example of a multifractal system. It is typically drawn in three dimensions for illustrative purposes. == Generation == The iteration applies to vector ''z'' as follows: function iterate(''z''): for each component in ''z'': if component > 1: component := 2 - component else if component < -1: component := -2 - component if magnitude of ''z'' < 0.5: ''z'' := ''z'' * 4 else if magnitude of ''z'' < 1: ''z'' := ''z'' / (magnitude of ''z'')^2 ''z'' := ''scale'' * ''z'' + ''c'' Here, ''c'' is the constant being tested, and ''scale'' is a real number. A notable property of the mandelbox, particularly for scale -1.5, is that it contains approximations of many well known fractals within it.〔(negative-mandelbox )〕〔(more-negatives )〕〔(mandelbox_3d_fractal )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mandelbox」の詳細全文を読む スポンサード リンク
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