Fractals/Mathematics for computer graphic

Update completion indicators "It can be argued that the mathematics behind these images is even prettier than the pictures themselves." Robert L. Devaney "We choose to do mathematics, not because it is easy, but because it is hard." user "Haskell Curry " You don't need to be a mathematician to appreciate the impressive beauty of fractals, and many times intuition and curiosity are two of the more important ingredients that drive mathematical discovery. Víctor José García Garrido "whereas mathemathical idea is a timless thing, few things are more ephemeral then computer hardware and software" Tristan Needham in Visual Complex Analysis Mathematics for computer graphic 00% Numbers by base 100% binary number decimal 00% sequences 00% Period 00% Continued fraction 00% Function, map, iterated function angle doubling map rotating map Complex quadratic map rational map Derivative 00% computations 00% Numerical methods, precision, error 00% Finding roots of equation 00% Newton method Durand-Kerner method 00% Finding function from sequence , curve fitting, model fitting 00% Symbolic methods 00% Kneading sequences 00% Group theory 00% Binary adding group 00% Basilica group 00% Kleinian group 00% Vector field 00% Polynomial vector field in one complex variable 00% Line integral convolution ( LIC) global visualisation of vector field 00% From discrete dynamical systems to continuous dynamical systems 00% dynamical system 00% discrete map 00% difference equation 00% differential equation Computational topology topology of point cloud data ( PCD) from PCD to simplicial complexes surface topology: Normal curves and surfaces, Paths in the plane Topological graph theory, Computation of Contour Trees and Topology of Level Sets distance fields: SDF noise Morse theory relates critical points of a function on a manifold (geometry) to the topology of the manifold 00% Computational Geometry has immediate applications in many other research areas, including computer graphics, mesh generation, geographic information systems, VLSI design, and robotics Specific problems convex hulls Voronoi diagrams line segment intersection polygon triangulation geometric range searching low-dimensional linear programming geometric shortest paths visibility parts Discrete geometry ( it includes Digital geometry = computer graphics and image analysis, Geometry processing = mesh processing ) computational conformal geometry Discrete Differential Geometry 00% Hyperbolic geometry software cgal The Computational Geometry Algorithms Library