Particle Systems—a Technique for Modeling a Class of Fuzzy Objects
ACM Transactions on Graphics (TOG)
Computer rendering of stochastic models
Communications of the ACM
Simulation of wrinkled surfaces
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Towards an interactive high visual complexity animation system
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
Plants, fractals, and formal languages
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Simulation of natural scenes using textured quadric surfaces
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Stochastic modeling in computer graphics
Stochastic modeling in computer graphics
Computer Generation of Texture Using a Syntactic Approach
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Real time design and animation of fractal plants and trees
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Combinatorial analysis of ramified patterns and computer imagery of trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Efficient antialiased rendering of 3-D linear fractals
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Representation of fractal curves by means of L systems
APL '96 Proceedings of the conference on Designing the future
Harnessing chaos for image synthesis
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Koch Curves as Attractors and Repellers
IEEE Computer Graphics and Applications
Programming Languages for Compressing Graphics
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Minimum Communication Cost Fractal Image Compression on PVM
Proceedings of the 6th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
IFS Fractal Interpolation for 2D and 3D Visualization
VIS '95 Proceedings of the 6th conference on Visualization '95
Fast Fractal Image Compression
ITCC '00 Proceedings of the The International Conference on Information Technology: Coding and Computing (ITCC'00)
Towards Realistic Modeling and Rendering of 3-D Escape-Time Deterministic Fractal Shapes
VSMM '01 Proceedings of the Seventh International Conference on Virtual Systems and Multimedia (VSMM'01)
Real-time rendering of plant leaves
ACM SIGGRAPH 2005 Papers
Real-time rendering of plant leaves
ACM SIGGRAPH 2006 Courses
Encoding images through transition probabilities
Mathematical and Computer Modelling: An International Journal
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In computer graphics, geometric modeling of complex objects is a difficult process. An important class of complex objects arise from natural phenomena: trees, plants, clouds, mountains, etc. Researchers are at present investigating a variety of techniques for extending modeling capabilities to include these as well as other classes. One mathematical concept that appears to have significant potential for this is fractals. Much interest currently exists in the general scientific community in using fractals as a model of complex natural phenomena. However, only a few methods for generating fractal sets are known. We have been involved in the development of a new approach to computing fractals. Any set of linear maps (affine transformations) and an associated set of probabilities determines an Iterated Function System (IFS). Each IFS has a unique "attractor" which is typically a fractal set (object). Specification of only a few maps can produce very complicated objects. Design of fractal objects is made relatively simple and intuitive by the discovery of an important mathematical property relating the fractal sets to the IFS. The method also provides the possibility of solving the inverse problem. given the geometry of an object, determine an IFS that will (approximately) generate that geometry. This paper presents the application of the theory of IFS to geometric modeling.