Title: Shape Formation Through Cell Growth and Gradient Exudation
1Shape 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
2Overview
- Goals
- Description of environment
- Creating shapes without direction
- Bootstrapping, determining the goodness' of
cells - Future work
3Goals
- 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
4Environment 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
5Environment 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
6Environment 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
7How 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
8Without 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
9General 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
10Example 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
11Getting 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
12Getting 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'
13Qualities 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
14Future 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