To Live and Die in CA
description
Transcript of To Live and Die in CA
![Page 1: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/1.jpg)
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
![Page 2: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/2.jpg)
INTRODUCTION TO
CA(CELLULAR AUTOMATA)
To Live and Die in CA
![Page 3: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/3.jpg)
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
![Page 4: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/4.jpg)
To Live and Die in CA
Neighborhoods
Moore von Neumann
![Page 5: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/5.jpg)
To Live and Die in CA
radius=3radius=1
target square
![Page 6: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/6.jpg)
To Live and Die in CA
Neighborhoods
Radius = 1 Radius = 3
![Page 7: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/7.jpg)
BIOLOGICAL CA MODELS
To Live and Die in CA
![Page 8: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/8.jpg)
To Live and Die in CA
Cellular Automata – Why do we want to do this?
5 steps
40 steps
![Page 9: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/9.jpg)
Biovermiculation with Discontinuities
CA Simulation
- Penny Boston
To Live and Die in CA
![Page 10: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/10.jpg)
To Live and Die in CA
CA Model of BiovermCave Bioverm photo courtesy of Penny
Boston
![Page 11: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/11.jpg)
THE NATURE OF GROWTH
IN
CELLULAR AUTOMATA
To Live and Die in CA
![Page 12: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/12.jpg)
To Live and Die in CA
Birth=1Radius=1Death=0Time=4
![Page 13: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/13.jpg)
To Live and Die in CA
![Page 14: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/14.jpg)
To Live and Die in CA
Birth=1Radius=1Death=0Time=5
![Page 15: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/15.jpg)
To Live and Die in CA
![Page 16: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/16.jpg)
To Live and Die in CA
Birth=1Radius=1Death=0Time=4
![Page 17: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/17.jpg)
To Live and Die in CA
![Page 18: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/18.jpg)
To Live and Die in CA
Birth=1Radius=1Death=0Time=4
![Page 19: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/19.jpg)
To Live and Die in CA
![Page 20: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/20.jpg)
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
![Page 21: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/21.jpg)
FRACTALCA
To Live and Die in CA
![Page 22: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/22.jpg)
To Live and Die in CA
Fractal CABirth=1 Death>2Radius=1Line start
![Page 23: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/23.jpg)
To Live and Die in CA
Fractal CABirth=1 Death>2Radius=1Line start
This time step:Blue=new growthRed=deathGreen=residual growth
![Page 24: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/24.jpg)
To Live and Die in CA
Fractal CABirth=1 Death>3Radius=1Line start
![Page 25: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/25.jpg)
To Live and Die in CA
This time step:Blue=new growthRed=deathGreen=residual growth
Fractal CABirth=1Death>1Radius=1Square start
![Page 26: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/26.jpg)
CA L-SYSTEM
GRAMMAR
To Live and Die in CA
![Page 27: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/27.jpg)
To Live and Die in CA
L-system CA Graphical Forms & Symbols
![Page 28: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/28.jpg)
To Live and Die in CA
L-system CA Symbols: Modifiers & Movement
![Page 29: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/29.jpg)
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
![Page 30: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/30.jpg)
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
![Page 31: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/31.jpg)
CA L-SYSTEM PRODUCTIONS
To Live and Die in CA
![Page 32: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/32.jpg)
To Live and Die in CA
![Page 33: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/33.jpg)
To Live and Die in CA
![Page 34: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/34.jpg)
FUTURE RESEARCH DIRECTIONS
To Live and Die in CA
![Page 35: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/35.jpg)
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.
![Page 36: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/36.jpg)
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.
![Page 37: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/37.jpg)
THANK YOUFOR
ATTENDING
To Live and Die in CA
![Page 38: To Live and Die in CA](https://reader035.fdocuments.us/reader035/viewer/2022081516/56814871550346895db57d0a/html5/thumbnails/38.jpg)
To Live and Die in CA