|
In mathematics, a multibrot set is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by a member of the general monic univariate polynomial family of recursions.〔(【引用サイトリンク】title=Definition of multibrots )〕〔(【引用サイトリンク】title=Multibrots )〕 The name is a portmanteau of multiple and Mandelbrot set. : where ''d'' ≥ 2. The exponent ''d'' may be further generalized to negative and fractional values. Several graphics are available but, as far as can be verified, none of these have been taken a step further to display a 3-D stack of the various stages so that the evolution of the general shape can be seen from other than vertically above. ==Examples == The case of : is the classic Mandelbrot set from which the name is derived. The sets for other values of ''d'' also show fractal images〔(【引用サイトリンク】title=Animated morph of multibrots ''d'' = −7 to 7 )〕 when they are plotted on the complex plane. Each of the examples of various powers ''d'' shown below is plotted to the same scale. Values of ''c'' belonging to the set are black. Values of ''c'' that have unbounded value under recursion, and thus do not belong in the set, are plotted in different colours, that show as contours, depending on the number of recursions that caused a value to exceed a fixed magnitude in the Escape Time algorithm. 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「Multibrot set」の詳細全文を読む スポンサード リンク
|