1 Graphical modeling using L-systems.- 1.1 Rewriting systems.- 1.2 DOL-systems.- 1.3 Turtle interpretation of strings.- 1.4 Synthesis of DOL-systems.- 1.4.1 Edge rewriting.- 1.4.2 Node rewriting.- 1.4.3 Relationship between edge and node rewriting.- 1.5 Modeling in three dimensions.- 1.6 Branching structures.- 1.6.1 Axial trees.- 1.6.2 Tree OL-systems.- 1.6.3 Bracketed OL-systems.- 1.7 Stochastic L-systems.- 1.8 Context-sensitive L-systems.- 1.9 Growth functions.- 1.10 Parametric L-systems.- 1.10.1 Parametric OL-systems.- 1.10.2 Parametric 2L-systems.- 1.10.3 Turtle interpretation of parametric words.- 2 Modeling of trees.- 3 Developmental models of herbaceous plants.- 3.1 Levels of model specification.- 3.1.1 Partial L-systems.- 3.1.2 Control mechanisms in plants.- 3.1.3 Complete models.- 3.2 Branching patterns.- 3.3 Models of inflorescences.- 3.3.1 Monopodial inflorescences.- 3.3.2 Sympodial inflorescences.- 3.3.3 Polypodial inflorescences.- 3.3.4 Modified racemes.- 4 Phyllotaxis.- 4.1 The planar model.- 4.2 The cylindrical model.- 5 Models of plant organs.- 5.1 Predefined surfaces.- 5.2 Developmental surface models.- 5.3 Models of compound leaves.- 6 Animation of plant development.- 6.1 Timed DOL-systems.- 6.2 Selection of growth functions.- 6.2.1 Development of nonbranching filaments.- 6.2.2 Development of branching structures.- 7 Modeling of cellular layers.- 7.1 Map L-systems.- 7.2 Graphical interpretation of maps.- 7.3 Microsorium linguaeforme.- 7.4 Dryopteris thelypteris.- 7.5 Modeling spherical cell layers.- 7.6 Modeling 3D cellular structures.- 8 Fractal properties of plants.- 8.1 Symmetry and self-similarity.- 8.2 Plant models and iterated function systems.- Epilogue.- Appendix A Software environment for plant modeling.- A.1 A virtual laboratory in botany.- A.2 List of laboratory programs.- Appendix B About the figures.- Turtle interpretation of symbols.

/pdf/the-algorithmic-beauty-of-plants-4f9yunhil9.pdf

The Algorithmic Beauty of Plants

The braid groups are infinite non-commutative groups naturally arising from geometric braids The aim of this article is twofold One is to show that the braid groups can serve as a good source to enrich cryptography The feature that makes the braid groups useful to cryptography includes the followings: (i) The word problem is solved via a fast algorithm which computes the canonical form which can be efficiently manipulated by computers (ii) The group operations can be performed efficiently (iii) The braid groups have many mathematically hard problems that can be utilized to design cryptographic primitives The other is to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in the braid groups The efficiency of our systems is demonstrated by their speed and information rate The security of our systems is based on topological, combinatorial and group-theoretical problems that are intractible according to our current mathematical knowledge The foundation of our systems is quite different from widely used cryptosystems based on number theory, but there are some similarities in design

/pdf/new-public-key-cryptosystem-using-braid-groups-4jt4e0sw77.pdf

New Public-Key Cryptosystem Using Braid Groups

The aim of this chapter is to generalize concepts and techniques of formal language theory to two dimensions. Informally, a two-dimensional string is called a picture and is defined as a rectangular array of symbols taken from a finite alphabet. A two-dimensional language (or picture language) is a set of pictures.

Two-dimensional languages

This paper selectively surveys contributions to major topics in pattern recognition since 1968. Representative books and surveys pattern recognition published during this period are listed. Theoretical models for automatic pattern recognition are contrasted with practical,, design methodology. Research contributions to statistical and structural pattern recognition are selectively discussed, including contributions to error estimation and the experimental design of pattern classifiers. The survey concludes with a representative set of applications of pattern recognition technology.

Patterns in pattern recognition: 1968-1974

A new method for generating pictures is presented and illustrated with examples. The idea is to generate a string of symbols using an L−system, and to interpret this string as a sequence of commands which control a "turtle". Suitable generalizations of the notions of the L−system and of a turtle are introduced. The resulting mathematical model can be used to create a variety of (finite approximations of) fractal curves, ranging from Koch curves, to classic space−filling curves, to relatively realistic−looking pictures of plants and trees. All these pictures are defined in a uniform and compact way.

http://algorithmicbotany.org/papers/graphical.gi86.pdf

Graphical applications of L-systems

Abstract families of matrices and picture languages

Generative models of picture languages with array rewriting rules are presented. The rewriting rules are regular, context-free or context-sensitive with arrays of terminals in the place of strings of terminals. Derivations are restricted by the condition for row and column catenation. The grammars describe a wide variety of pictures and are more powerful than the matrix grammars for digital pictures introduced in our earlier paper. A distinct hierarchy is shown to exist between the different classes introduced. The models are closed under reflection (about base and rightmost vertical), halfturn, quarter-turn, transpose, and conjugation. Further closure properties such as union, product, star and homomorphism are examined. The models can be applied to generate several interesting patterns of kolam and to describe the repetitive patterns of two-dimensional crystallography. Each letter of the alphabet of different sizes can be generated by a context-free array grammar.

Picture languages with array rewriting rules

Array Grammars and Kolam

A generative grammar called equal matrix grammar which generates a class which meets both context-sensitive and context-free languages is defined and the formal power series generated by context-free grammars is extended to grammars of this system. The Parikh mapping of this family of languages is shown to be semilinear. The Boolean and closure properties of a certain subfamily are examined. For this subfamily, the generative power of equal matrix grammar is higher than that of context-free grammars. For certain inherently ambiguous context-free languages, including that of Parikh, unambiguous grammars of this class exist. The application of equal matrix grammar to the generation of Tamil kernel sentences is given in the appendix.

On equal matrix languages

Circular strings representing DNA molecules and certain recombinant behaviour are formalized. Various actions of splicing schemes on linear and circular DNA molecules are examined. It is shown that there is a difference in the regularity result of Culik and Harju [1] between the linear and circular strings. A consequence of this result is that a conjecture of Head [4] that the circular string language of a splicing system under an action on circular strings is regular, when the set of initial circular strings is regular, is disproved.

Rani Siromoney

Papers

Abstract families of matrices and picture languages

Picture languages with array rewriting rules

Array Grammars and Kolam

On equal matrix languages

Circular DNA and Splicing Systems