Cellular Automata Modeling Environment

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CellularAutomataModelingEnvironment Library

• Lev Naumov
• levnaumov_at_mail.ru

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What Is CAMEL?

• Environment, which allows to research, visualize
  and solve problems, basing cellular automata
  concept
• Tool for distributed parallel computations and
  study of parallel algorithms
• Library, which represents rich toolkit for
  building solutions

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What Are Cellular Automata?

• Cellular automata simple models, which are used
  for studying complex systems behavior in
  different fields of science
• These automata are discrete dynamic systems,
  which work can be completely described in the
  terms of local interactions
• Cellular systems form common paradigm of parallel
  computations as Turing machines do for the
  consecutive computations

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What for Cellular Automata Are Applicable?

• For modeling of processes or distributed systems
  in physics, mathematics, computer sciences,
  chemistry, biology, psychology, meteorology,
  social sciences and other fields of science
• Cellular automaton is discrete analogue of
  field concept
• For using as spaces of parallel computations for
  tasks solving

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Why Cellular Automata?

• Common and most simple models of parallel
  computations
• Parallel tasks are urgent and important
• Throughput of single processor is limited by
  technological causes
• There are a lot of heavy tasks which can and
  need to be solved using parallel computations
• There are a lot of tasks which are based on
  space-distributed computer systems

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Definition of Cellular Automaton

• Cellular automaton A is a set of four objectsA
  ltG, Z, N, fgt, where
• G grid, set of cells
• Z set of possible cells states
• N set, which describes cells neighborhood
• f transition function, rules of the automaton
• ZN1?Z (for automaton, which has cells with
  memory)
• ZN?Z (for automaton, which has memoryless
  cells)

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Two-Dimensional Grids

• Cells that have a common edge with the involved
  are named as main neighbors of the cell (are
  showed with hatching)
• The set of actual neighbors of the cell a, which
  can be found according to N, is denoted as N(a)

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Basic Cellular Automata Properties

• Transition function is to be local
• System is to be similar for all the cells
• To avoid side effects grid can use boundary
  conditions
• Torus
• Mobius band
• Constant
• All cells get their new values simultaneously, at
  the end of the timestep, after all new values
  were calculated for all cells

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Definition of the Rings

• Ring is the set of cells. It can be introduced
  for each cell on the grid
• Let us assume the cell itself to be its cell of
  the zero ring and its nearest neighbors to be the
  cells of first ring of the involved cell
• For the current cell, its cells of the i-th ring
  are nearest neighbors of members of (i1)-th
  ring, excluding cells of (i1)-th and (i2)-th
  rings

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Definition of the Rings

• Formally, if R(a, i) is a set of cells of i-th
  ring of cell a, then if N describes cells
  neighborhood as the set of its nearest neighbors,
  following formula will take place

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Rings for Grid of Triangles

• Different rings are showed with hatching or color

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Rings for Grid of Squares

• Different rings are showed with hatching or color

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Rings for Grid of Hexagons

• Different rings are showed with hatching or color

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Definition of the Metrics

• Distance function D(a, b) for retrieving
  remoteness between cells a and b can be denoted
  as follows

It is proved that this function satisfies to all
metrics properties The notion of ring may be
generalized for multi-dimensional grids and the
distance function, given by last formula, will
remain the same
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The Problem

• Cellular automaton is specific parallel
  architecture so it needs specific hardware or at
  least software platform
• Multifunctional environment for solving problems
  with the help of cellular automata will allow to
  use computers as
• assembly for physical, chemical, biological and
  other experiments (may be very expensive)
• tool for execution, visualization and analysis of
  parallel computations

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CAMEL

• Cellular
• Automata
• Modeling
• Environment
• Library

Windows-based software, that is desired to be
simple, extensible workspace for complicated
cellular calculations
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Why CAMEL?

• Existing products put limitations over automata
  that can be used
• Majority of existing products do not satisfy
  modern requirements to user interface and do not
  support contemporary technologies
• Many existing products have complicated languages
  for cellular automata description

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Advantages of CAMEL

• Existing products put limitations over automata
  that can be used
• Majority of existing products do not satisfy
  modern requirements to user interface and do not
  support contemporary technologies
• Many existing products have complicated languages
  for cellular automata description

• No limitations at all
• Handy user interface with the support of useful
  features
• C or any other language that was developed

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CAMEL Components

• Each experiment is controlled and implemented by
  components
• Components may be used in different combinations
  and add arbitrary functionality
• Each component declares list of its parameters
  which are used for the tuning
• Each component is a dynamic link library
• Components are to be realized using Cellular
  Automata Developing Library (CADLib)

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CADLib

• For CADLib User Developer Researcher
• CADLib presents rich set of instruments for
  components development
• This is a ? class library for further enlarging
  and reusing
• It also contains some useful functions, constants
  and macrodefinitions

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CADLib
Rich and well structured class hierarchy provides
easy-to-use and powerful toolkit It makes
possible to customize all necessary behavior of
system
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CAMEL Components

• Each automaton consists of four components
• Grid implements visualization of grid and cells
  navigation
• Datum maintains data storage
• Metrics provides the relationship of
  neighborhood, distance function and assigns
  coordinates to cells
• Rules describes computations (initialization,
  iteration and finalization)
• Other type of components
• Analyzer allows to keep an eye on definite
  properties of automaton

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Why Is Separate Metrics Component Needed?

• It was possible to place necessary functionality
  to the datum component
• Metrics is separate component because this fact
  gives opportunity to use non-standard coordinate
  systems. For example, generalized coordinates

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What is Generalized Coordinates?

• The idea is to enumerate all cells of the grid.
  It must be done without any blanks. Each number
  is to have one and only one corresponding cell
• There must be the way to find cells nearest
  neighbors. It will be enough to work with any
  neighborhood
• The method of associating cells with generalized
  coordinates can be different. The main aim is to
  introduce them in the way, which allows to
  retrieve cells neighbors as fast as possible

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Spiral Generalized Coordinates for Hexagonal Grid

• Choose any cell as zero cell and then enumerate
  cells in each its ring clockwise
• There are formulae for retrieving coordinates of
  nearest cells in this metrics

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Generalized Coordinates for Grid of Triangles

• After applying spiral generalized coordinates for
  hexagons, each triangles coordinate can be got as
  coordinate of hexagon, multiplied by six and
  added index of triangle inside the hexagon

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Generalized Coordinates for Grid of Triangles

• In this metrics there is no need to consider two
  variants of cells orientation separately
• Tests shows, that this way of introducing of
  generalized coordinates for the grid of triangles
  allows to calculate the nearest neighbor cells
  several times faster than a spiral way for this
  grid. The cause is in
• complexity of a ring for the grid of triangles
• recursion which is used for spiral coordinates of
  non-main cells neighbors, but in the grid of
  hexagons all cells neighbors are main

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Generalized Coordinates Based on Composite
Cubicles

• Useful for performance optimization
• as for triangular grid based on hexagonal
  cubicles
• Allows to introduce coordinates for complicated
  grids
• as the soccer ball grid

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Spiral Generalized Coordinates

• There are formalisms of spiral generalized
  coordinates for all three possible
  two-dimensional grids of regular polygons
• This concept may be used for multidimensional
  and more complicated grids

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Generalized Coordinates Disadvantage and
Advantages

• Main disadvantage of the offered approach is that
  calculations of neighbors are slower than, for
  example, for the Cartesian case

• Generalized coordinates provide a universal way
  of data storage for different grids
• Grid may be easily enlarged if it is necessary
• Serial data is easier to serialize and store
• Independency from the zero-cells position gives
  the opportunity to move it to the place where it
  would be more useful
• Generalized coordinates is just a concept, so it
  could be adopted for the definite task

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Generalized Coordinates for Parallel Computations

• Cellular automata are the models of parallel
  computations with infinite extent of parallelism.
  Using the generalized coordinates the system with
  infinite extent of parallelism can be emulated
  with the help of several interacting Turing
  machines. A single machine used to work with data
  storage (the tape) and other machines are used
  for neighbors calculations and synchronization

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Rules Component Functions

• Other existing projects
• Rules Transition function
• Use many languages for transition functions
  description

• CAMEL
• Rules component fully describes computations
• Method of parallelization
• Computations optimization
• Transition function
• Single rules component may represent a parser of
  language for transition functions description and
  work with arbitrary transition functions (not
  with only one)

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Analysis of Experiment

• Rules component declares list of values which are
  interesting for the researcher
• These values are calculated during the iteration
• Analyzer component allows to study these values
  changing
• Draw graphs
• Build reports to file

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Cellular Automata Properties In CAMEL

• Transition function is to be local
• System is to be similar for all the cells
• To avoid side effects grid can use boundary
  conditions
• All cells get their new values simultaneously, at
  the end of the timestep, after all new values
  were calculated for all cells

• Transition function can be not local
• System can be not similar for all the cells
• Standard datum components allows to select
  boundary conditions
• Each cells can get new value just after it was
  calculated

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CAMEL Features

• Allows to use arbitrary automata without any
  limitations
• Has handy rich user interface. Supports
• Undo-redo functionality
• Clipboard operations
• Printing, saving pictures for illustrating
  articles
• Many many other features
• Stores data in XML files, that can become
  standard for cellular information interchange
• Can compress data on the fly using BZip2 algorithm

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CAMEL Features

• Has multidocument interface
• allows to work with several automata
  simultaneously
• allows to implement automata interactions
• Has rich toolkit to control, study and analyze
  the experiment
• Allows to build graphs of computations
  performance
• Is provided with examples of different
  components, which can be used for users tasks
  solving or as a basis of users components

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CAMEL Features

• Allows to perform parallel computations
• On multiprocessor computer
• On cluster
• Allows to arrange clusters
• In local area network
• In the Internet
• Uses novel network Commands Transfer Protocol
  (CTP) for cluster computations
• Fast, reliable and featureful

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CAMEL Project

• Project was announced on International Conference
  on Computational Sciences 2003 (Melbourne
  Saint-Petersburg, June 2003) and attracts
  interest of scientists
• The work is in progress