an investigation into the nature of growth in elementary cellular automata to live and die in ca by...
TRANSCRIPT
AN INVESTIGATION INTO THE NATURE OF GROWTH IN
ELEMENTARY CELLULAR AUTOMATA
To Live and Die in CA
by Jane Curnutt
Committee:Yasha Karant, advisorErnesto GomezKeith Schubert
INTRODUCTION TO
CA(CELLULAR AUTOMATA)
To Live and Die in CA
To Live and Die in CA
CA VocabularyDeterministicSynchronousTotalisticGrid (like a piece
of graph paper)Neighborhood
Moore Neighborhood
von Neumann Neighborhood
Calculation Radius
(Radius)Target SquareRules:
birth=n1 death>n2
To Live and Die in CA
Neighborhoods
Moore von Neumann
To Live and Die in CA
radius=3radius=1
target square
To Live and Die in CA
Neighborhoods
Radius = 1 Radius = 3
BIOLOGICAL CA MODELS
To Live and Die in CA
To Live and Die in CA
Cellular Automata – Why do we want to do this?
5 steps
40 steps
Biovermiculation with Discontinuities
CA Simulation
- Penny Boston
To Live and Die in CA
To Live and Die in CA
CA Model of BiovermCave Bioverm photo courtesy of Penny
Boston
THE NATURE OF GROWTH
IN
CELLULAR AUTOMATA
To Live and Die in CA
To Live and Die in CA
Birth=1Radius=1Death=0Time=4
To Live and Die in CA
To Live and Die in CA
Birth=1Radius=1Death=0Time=5
To Live and Die in CA
To Live and Die in CA
Birth=1Radius=1Death=0Time=4
To Live and Die in CA
To Live and Die in CA
Birth=1Radius=1Death=0Time=4
To Live and Die in CA
To Live and Die in CA
ConclusionsGrowth only takes place at endpoints and vertices
Growth is always perpendicular to the growth in previous time step
Growth is recursive
FRACTALCA
To Live and Die in CA
To Live and Die in CA
Fractal CABirth=1 Death>2Radius=1Line start
To Live and Die in CA
Fractal CABirth=1 Death>2Radius=1Line start
This time step:Blue=new growthRed=deathGreen=residual growth
To Live and Die in CA
Fractal CABirth=1 Death>3Radius=1Line start
To Live and Die in CA
This time step:Blue=new growthRed=deathGreen=residual growth
Fractal CABirth=1Death>1Radius=1Square start
CA L-SYSTEM
GRAMMAR
To Live and Die in CA
To Live and Die in CA
L-system CA Graphical Forms & Symbols
To Live and Die in CA
L-system CA Symbols: Modifiers & Movement
To Live and Die in CA
Why we need an SP character in the grammar?Square Inside the
2r+1 Radiusred - neighborhoodred - target square green - current time
step blue – growth next
time step
To Live and Die in CA
red - neighborhoodred - target square
green - current time step
blue – growth next time step
Square Outside the 2r+1 Radius
CA L-SYSTEM PRODUCTIONS
To Live and Die in CA
To Live and Die in CA
To Live and Die in CA
FUTURE RESEARCH DIRECTIONS
To Live and Die in CA
To Live and Die in CA
Extend CA grammar to include death rules.
Investigate the relationship between CA grammar and display grid, with different grids.
Investigate collisions between patterns, and whether CA grammar can describe them.
To Live and Die in CA
Special thanks to Chris McKay,
Principle Investigator for Extreme Environments,NASA, Ames
and
Penny Boston, NMITAssociate Director,
National Cave and Karst Research Institute,
for their support and encouragement.
THANK YOUFOR
ATTENDING
To Live and Die in CA
To Live and Die in CA