Analysis on the Cause and Influence of Fractal:In Memory of the 100th Anniversary of Mandelbrot's Birthday
In the later period of analysis rigor,many ill conditioned mathematical objects such as Weierstrass function,Cantor set,Koch curve and so on continue to emerge,and mathematical problems related to them also emerge in endlessly.Driven by these problems,Hausdorff and other mathematicians created and improved the theory of fractional dimension.Cesàro and other mathematicians established and developed the self-similarity theory.At the same time,practical issues such as the paradox of coastline length also emerge one after another.The interaction between internal and external factors led Mandelbrot to extract commonalities from individuality,search for order from disorder,embed internal essence from external appearances,deeply solve problems,abstract and sublimate theory,and ultimately establish fractal geometry.The strict concept of fractal has undergone evolution and is still being explored to this day.The fractal dimension and self similarity features based on infinitesimal theory and nonlinear thinking reveal its connotation and exten-sion.Although fractal,as a new thing,was opposed at the beginning of its establishment,its own unique excellent attributes will certainly make it perfect in the future.
history of mathematicsfractalfractional dimensionMandelbrot
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