Fractal geometry and computer graphics
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with actual trends and topics of future research, are reported in the last section. The topics of the book are divides into four sections: Fundamentals, Computer Graphics and Optical Simulation, Simulation of Natural Phenomena, Image Processing and Image Analysis.
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1/f Noise ACM Computer Graphics algorithm analysis application attractor automaton behaviour boundary Bremen Brownian motion bubble calculated cell cellular automata circles clouds color complex Computer Graphics cubes data points data-sets defined definition dendrone denote described deterministic distance equation escape-time example exponent Figure finite Fourier fractal dimension Fractal Geometry Fractal Images fractal model fractal set frequency grid Hausdorff dimension HiLDTe individualists integration of fractals interpolation iterated function systems Julia sets Koch curve language LRIFS Mandelbrot set mapping mathematical matrix substitution system method metric space n-adic-HIFS natural noise normal vector objects parameters pattern Peitgen phase picture pixels Plate polygons prepigments productivity properties radius random fractals recursive rendering resolution result Saupe scaling selfsimilarity sequence shows Sierpinsky triangles Simulation snapshot FLASH space spectral spectrum step structure surface techniques texture elements texture synthesis theory tion trajectory transformation tumor turbulence values velocity visual ymax ymin Zp[x