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Shape Formation Through Cell Growth and Gradient Exudation

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Shape Formation Through. Cell Growth and Gradient Exudation ... Phi is the measure of how good a cell's location is compared to the location we would like ... – PowerPoint PPT presentation

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Title: Shape Formation Through Cell Growth and Gradient Exudation


1
Shape Formation ThroughCell Growth and Gradient
Exudation
  • Growing arbitrary shapes with more fun
  • than you can shake a caml at!
  • Christopher Frost
  • chris_at_zurich.ai.mit.edu
  • Massachusetts Institute of Technology /
  • University of Virginia

2
Overview
  • Goals
  • Description of environment
  • Creating shapes without direction
  • Bootstrapping, determining the goodness' of
    cells
  • Future work

3
Goals
  • Develop a method of constructing arbitrary shapes
    using only cells which have no concept of
    direction and can
  • Divide
  • Commit suicide
  • Exude and react to gradients
  • Create circles from circles creating and using
    reference points'
  • Work in 2D

4
Environment Description
  • Cell Primitives
  • Division/Having children
  • Defines one's 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 we're shooting for, but
    easier for now
  • When a cells reads a gradient it knows
  • the gradient's id, the strength of the
    gradient here, and the exuder's phi value

5
Environment Description, cont
  • Cells are immobile
  • Cells can't overlap
  • No concept of orientation of a cell or a global
    notion of direction
  • Gradients spread instantly
  • Gradients allow measurement of exact distance

6
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

7
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

8
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

9
General Location Goodness' Algorithm
  • Phi is the measure of how good a cell's 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

10
Example of Defining a Reference Point
Create a reference point with the id 3 whose
gradient travels the diameter of the circle uses
gradients 4, 1, 0, and 2, the ratios ... , and
triangulation to position itself
11
Getting Cells to Figure OutWho Has the Best Phi
Value
  • 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

12
Getting Cells to Figure OutWho Has the Best Phi
Value, cont
  • Listen and exude
  • Every cell listens to gradients it can hear
  • Finds phi value for every gradient it could
    create from these hearable gradients
  • 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, grad is heard
  • we fall out of the phi range'

13
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 gradient moves, gradients which depend on
    this gradient can move

14
Future Work
  • The near future
  • Finish implementing multiple circle creation
  • (Implement ideas for cell death and growth
    restart)
  • Read Catie's program's datastructure
  • Ideas to look into
  • Possibly optimizing when should cells die
  • Dynamic gradient dependent determination / robust
    shape recreation
  • Introducing more perturbations and testing
    robustness
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