.MCAD 304020000 1 74 16274 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.197917 1.000000 1.000000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=528
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=528
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=2 family=Century^Schoolbook points=12 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
.CMD COLORTAB_ENTRY 255 0 0
.CMD COLORTAB_ENTRY 0 255 0
.CMD COLORTAB_ENTRY 255 255 0
.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
.CMD COLORTAB_ENTRY 255 255 255
.CMD COLORTAB_ENTRY 0 64 128
.TXT 3 10 16209 0 0
Cg a58.125000,58.125000,30
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2\fs32 CELLULAR AUTOMATA AND FRACTALS}}
.TXT 6 -9 3 0 0
Cg a71.750000,71.750000,340
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2 Cellular Automata which were invented by Ulam and von Neumann and 
further developed by Wolfram, are used extensively to model }{\cf2\b\i
\ul complex}{\cf2  temporal and spatial patterns in nature.\par I. }{
\cf2\b\ul Sierpinsky Gasket}{\cf2 :}{\cf2  We simulate the growth of 
the best known fractal, the Sierpinsky gasket. We will use complex 
numbers to represent the positions of the points.}{\cf2 \par }}
.TXT 18 14 16177 0 0
Cg a59.250000,59.250000,23
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard Triangle 
corners index:}
.EQN 0 27 16147 0 0
{0:m}NAME:0;3
.TXT 5 -27 16210 0 0
Cg a25.000000,25.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2 The corners of the triangle:}}
.EQN 0 27 16148 0 0
({0:T}NAME)[({0:m}NAME):({0:e}NAME)^(1i*(2*{0:\p}NAME)/(3)*{0:m}NAME)
.TXT 4 -27 16169 0 0
Cg a58.250000,58.250000,40
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2 Number of iterations:\par Iteration index n:}}
.EQN 0 27 16187 0 0
{0:N}NAME:5000
.EQN 3 0 16211 0 0
{0:n}NAME:1;{0:N}NAME
.TXT 3 -41 16159 0 0
Cg a55.750000,55.750000,59
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2 Generate a random interger: 0, 1, 2 with equal probability:}}
.EQN 0 56 16161 0 0
({0:u}NAME)[({0:n}NAME):{0:floor}NAME({0:rnd}NAME(3))
.TXT 3 -56 16172 0 0
Cg a18.250000,18.250000,19
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2 The starting point:}}
.EQN 0 58 16216 0 0
({0:P}NAME)[(0):0
.TXT 3 -58 16167 0 0
Cg a56.250000,56.250000,116
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2 Each point P}{\cf2\dn n}{\cf2  is located midway between the 
previous point P}{\cf2\dn n-1}{\cf2  and a randomly selected corner of 
the main triangle.}}
.EQN 1 58 16213 0 0
({0:P}NAME)[({0:n}NAME):0.5*(({0:P}NAME)[({0:n}NAME-1)+({0:T}NAME)[(({0:u}NAME)[({0:n}NAME)))
.EQN 4 -58 14 0 0
1&-1&(0&1)&{0:Im}NAME(({0:P}NAME)[({0:n}NAME)),{0:Im}NAME(({0:P}NAME)[(0)),{0:Im}NAME(({0:T}NAME)[({0:m}NAME))@&-1&(-1&1)&{0:Re}NAME(({0:P}NAME)[({0:n}NAME)),{0:Re}NAME(({0:P}NAME)[(0)),{0:Re}NAME(({0:T}NAME)[({0:m}NAME))
0 1 0 1 1 0 0 1 1 
0 1 0 1 1 0 0 1 1 
0 0 0 0 2 2 NO-TRACE-STRING
4 0 1 0 1 1 NO-TRACE-STRING
0 1 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 55 40 10 0 3 
.TXT 53 0 16218 0 0
Cg a73.250000,73.250000,29
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {\fs16 
COPYRIGHT: MIRON KAUFMAN 1997}}
.TXT 6 0 16208 0 0
Cg a72.500000,72.500000,381
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;\red0\green0\blue128;}{
\fonttbl{\f0\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {
\cf2\b\ul II. One-Dimensional Game of Life}{\cf2 : The most famous 
cellular automaton is Conway's Game of Life:  Start with a square 
lattice of cells which are either dead 0, or alive 1; at the next time 
cells that are alive die of overcrowding (too many neighbors) or of 
loneliness (too few neighbors).  We are going to simulate the time 
evolution of a one dimensional variant of the game of life.}}
.EQN 13 22 16232 0 0
{0:j}NAME:0;50
.TXT 4 -21 16227 0 0
Cg a72.250000,72.250000,32
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard Initial 
configuration is random:}
.EQN 0 34 16234 0 0
({0:x}NAME)[(0,{0:j}NAME):{0:floor}NAME({0:rnd}NAME(2))
.TXT 6 -34 16235 0 0
Cg a72.250000,72.250000,5
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard Time:}
.EQN 0 6 16236 0 0
{0:t}NAME:0;50
.EQN 4 0 16237 0 0
{0:j}NAME:1;49
.TXT 4 -6 16238 0 0
Cg a71.250000,71.250000,70
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard At the next 
time cells that have exactly one neighbor alive are alive:}
.EQN 4 5 16239 0 0
({0:x}NAME)[({0:t}NAME+1,{0:j}NAME):(({0:x}NAME)[({0:t}NAME,{0:j}NAME-1)+({0:x}NAME)[({0:t}NAME,{0:j}NAME+1))÷1
.EQN 4 -6 16200 0 0
{0:x}NAME{1 3 3 10 35 0 70 30 0 1 1 1 5 0 50 0 1 1 1 2 0 51 0 0 0 1 2 -1 1 5 0 16777215 1 100 2 NO-TITLE}{57}
2 5 21 21 0 1 1.5 7
1 5 4 3 0 4 1 0
3 1 2 0.1
.EQN 1 86 16274 0 0
255*{0:x}NAME{   25    45 0.000000 0.000000 0.000000 0.000000 0}{58}
.EQN 37 -86 16253 0 0
({0:meanx}NAME)[({0:t}NAME):(1)/(49)*((1,49,{0:j}NAME,({0:x}NAME)[({0:t}NAME,{0:j}NAME)){64})
.EQN 4 16 16257 0 0
1&0&(_n_u_l_l_&_n_u_l_l_)&({0:meanx}NAME)[({0:t}NAME)@50&&(_n_u_l_l_&_n_u_l_l_)&{0:t}NAME
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 47 15 10 0 3 
.TXT 22 -16 16268 0 0
Cg a73.250000,73.250000,29
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {\fs16 
COPYRIGHT: MIRON KAUFMAN 1997}}
.TXT 6 0 16242 0 0
Cg a73.250000,73.250000,84
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard We now use 
the same automaton but the initial configuration has only one cell alive.}
.EQN 5 7 16243 0 0
{0:j}NAME:0;50
.EQN 3 0 16202 0 0
({0:x}NAME)[(0,{0:j}NAME):{0:\d}NAME({0:j}NAME,25)
.EQN 4 0 16244 0 0
{0:t}NAME:0;50
.EQN 3 0 16204 0 0
{0:j}NAME:1;49
.EQN 3 0 16245 0 0
({0:x}NAME)[({0:t}NAME+1,{0:j}NAME):(({0:x}NAME)[({0:t}NAME,{0:j}NAME-1)+({0:x}NAME)[({0:t}NAME,{0:j}NAME+1))÷1
.EQN 5 -8 16206 0 0
{0:x}NAME{1 3 3 10 35 0 70 41 0 1 1 1 5 0 50 0 1 1 1 5 0 50 0 0 0 1 2 -1 1 5 0 16777215 1 100 2 NO-TITLE}{57}
2 5 21 21 0 1 1.5 7
1 5 4 3 0 4 1 0
3 1 2 0.1
.EQN 1 90 16272 0 0
255*{0:x}NAME{   36    43 0.000000 0.000000 0.000000 0.000000 0}{58}
.TXT 46 -89 16264 0 0
Cg a72.250000,72.250000,65
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard Note that 
the emmerging pattern looks like the Sierpinsky Gasket.}
.EQN 5 1 16265 0 0
({0:meanx}NAME)[({0:t}NAME):(1)/(49)*((1,49,{0:j}NAME,({0:x}NAME)[({0:t}NAME,{0:j}NAME)){64})
.EQN 1 15 16266 0 0
1&0&(_n_u_l_l_&_n_u_l_l_)&({0:meanx}NAME)[({0:t}NAME)@50&&(_n_u_l_l_&_n_u_l_l_)&{0:t}NAME
0 1 1 1 1 0 0 1 1 
0 1 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 47 15 10 0 3 
.TXT 25 -16 16269 0 0
Cg a73.250000,73.250000,29
{\rtf\ansi \deff0{\colortbl;\red0\green64\blue128;}{\fonttbl{\f0
\fcharset0\fnil Century Schoolbook;}}\plain\cf1\fs24 \pard {\fs16 
COPYRIGHT: MIRON KAUFMAN 1997}}