Shape Formation Through Cell Growth and Gradient Exudation

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Shape Formation ThroughCell Growth and Gradient
Exudation

• Growing arbitrary shapes with more fun
• than you can shake a caml at!
• Swarm _at_ UVa
• October 4th, 2002
• Christopher Frost
• frost_at_virginia.edu
• Massachusetts Institute of Technology /
• University of Virginia

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Overview

• Amorphous computing
• Goals
• Description of environment
• Creating shapes without direction
• Bootstrapping, determining the goodness of
  cells
• Shapes to descriptions
• Future work

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Amorphous Computing

• The defining characteristics of an amorphous
  system are
• Large numbers of identically programmed elements
• Limited computing power of individual elements
• Limited communication radius
• No a priori or global knowledge of the system
• No positional information

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Amorphous ComputingWhy Spatial Organization?

• This is a general example of how to organize an
  amorphous system
• Spatial differentiation is a clean way of showing
  differentiation of function
• Prevalence in biology

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Goals

• Develop a method of constructing arbitrary shapes
  using only cells which have no concept of
  direction and can
• Replicate
• Commit suicide
• Exude and react to gradients
• Create circles from circles creating and using
  reference points
• Work in 2D

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Environment Description

• Cell Primitives
• Replication/Having children
• Defines ones family
• Committing suicide
• Important because of positioning later on..
• Exuding and reacting to gradients
• Control amount of material exuded, determining
  how far a gradient will travel
• Not as realistic as were shooting for, but
  easier for now
• When a cells reads a gradient it knows
• corresponding reference id, the strength of
  the gradient here, and the exuder's phi value

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Environment Description, cont

• Cells are immobile
• Cells cant overlap
• No concept of orientation of a cell or a global
  notion of direction
• Gradients spread instantly
• Gradients allow measurement of exact distance

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Environment Simulator

• Was thread for every cell
• Now execs cell steps in random order (random
  subset of cells in each cycle)
• So methods can't depend on cells receiving
  gradients instantly
• Later reintroduce threads to exec fixed number
  of, but randomly chosen, cells at a time
• Cells sleep until a change in the environment
• Big speedup, most cells not executing most of the
  time
• Gradients can pass through voids, but we only
  use gradients that pass through cell areas

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How Do We Create Shapes Without The Notion of
Direction?

• We can create local coordinate systems in circles
  composed of cells
• Creating five reference points allows you to
  triangulate the closest cell within a circle to
  some position
• Including locations to grow new circles
• Five? Indeed, we will use all five in
  locating the first three reference points of
  additional circles

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Without Direction,How Do We Get The First Five
Points?

• First cell becomes the center
• Second reference point is an arbitrary
• point on the circumference
• Third reference point cell a certain distance
  from second reference point
• Fourth and fifth points triangulate using three
  existing points and be at least some minimum
  distance from each other
• Can now locate any point within the circle and
  triangulate points in the creation of new circles

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General Location Goodness Algorithm

• Phi is the measure of how good a cells location
  is compared to the location we would like
• A is the set of gradient values a particular
  cell reads and B is the set of gradient values
  one is trying to find
• Scale independent

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Example of Defining a Reference Point
Create a reference point with the id 3 whose
gradient travels the diameter of the circle uses
reference points 4, 1, 0, and 2, the ratios ...
, and triangulation to position itself
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Getting Cells to Figure OutWho Has the Best Phi
ValueA Fierce Competition

• Two methods explored
• cell hopping and listen and exude
• Cell hopping
• A cell asks its family for their phis, tells
  family the best phi value heard
• If you ask your family and you are the best, send
  the gradient and terminate
• Cell familiage often has separations, so this
  method can get stuck
• Many gradients sent

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Getting Cells to Figure OutWho Has the Best Phi
Value, cont

• Listen and exude
• Every cell listens to reference points it can
  hear
• Finds phi value for every gradient it could
  create using these hearable reference points
• If this value is within a certain range, the cell
  tries to become the gradient emitter
• If if no one else is exuding or this gradient is
  not being exuded with a better phi than ours
• this cell becomes the winner, exudes
• Stop exuding if
• another, better phied, gradient is heard
• we fall out of the phi range

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Qualities of theListen and Exude Method

• If a gradient disappears, someone else will pick
  it up
• Currently the first two points of the first
  circle are not recreateable, but once the first
  circle is created this can be changed
• If a reference point moves, reference points
  which depend on this reference point can move

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Shapes to Descriptions

• Describe an arbitrary shape by packing it with
  overlapping circles
• Three-phase compilation
• Finding an efficient circle covering (initial
  network)
• Constructing a tightly-linked network of circles
  by introducing intermediate circles
• Specifying position information in terms of
• distance ratios

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Future Work

• The near future
• Finish implementing multiple circle creation
• (Implement ideas for cell death and growth
  restart)
• Read Caties programs datastructure
• Ideas to look into
• Introducing more perturbations and testing
  robustness
• Possibly optimizing when should cells die
• Dynamic gradient dependent determination / robust
  shape recreation