Computer-simulated plant evolution
Scientific American
Real time design and animation of fractal plants and trees
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Graphical applications of L-systems
Proceedings on Graphics Interface '86/Vision Interface '86
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Construction of fractal objects with iterated function systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Approximate and probabilistic algorithms for shading and rendering structured particle systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Development models of herbaceous plants for computer imagery purposes
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Plant models faithful to botanical structure and development
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Interactive Animation: A Language and System for Procedural Modeling and Motion
IEEE Computer Graphics and Applications
A morphological study of the form of nature
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Procedure models for generating three-dimensional terrain
SIGGRAPH '80 Proceedings of the 7th 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
Artificial evolution for computer graphics
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
A Strahler bijection between Dyck paths and planar trees
Discrete Mathematics
A unified approach to the analysis of Horton-Strahler parameters of binary tree structures
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Fast construction of plant architectural models based on substructure decomposition
Journal of Computer Science and Technology
Approximate image-based tree-modeling using particle flows
ACM SIGGRAPH 2007 papers
Analytical study of a stochastic plant growth model: Application to the GreenLab model
Mathematics and Computers in Simulation
Quantifying the Degree of Self-Nestedness of Trees: Application to the Structural Analysis of Plants
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Comparison of methods for classification of breast ductal branching patterns
IWDM'06 Proceedings of the 8th international conference on Digital Mammography
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Herein is presented a new procedural method for generating images of trees. Many other algorithms have already been proposed in the last few years focusing on particle systems, fractals, graftals and L-systems or realistic botanical models. Usually the final visual aspect of the tree depends on the development process leading to this form. Our approach differs from all the previous ones. We begin by defining a certain "measure" of the form of a tree or a branching pattern. This is done by introducing the new concept of ramification matrix of a tree. Then we give an algorithm for generating a random tree having as ramification matrix a given arbitrary stochastic triangular matrix. The geometry of the tree is defined from the combinatorial parameters implied in the analysis of the forms of trees. We obtain a method with powerful control of the final form, simple enough to produce quick designs of trees without loosing in the variety and rendering of the images. We also introduce a new rapid drawing of the leaves. The underlying combinatorics constitute a refinment of some work introduced in hydrogeology in the morphological study of river networks. The concept of ramification matrix has been used very recently in physics in the study of fractal ramified patterns.