Summer 2010 CS61C Homework 2 : Life 1D

### Life 1D : Rule 30

You should read Wolfram's excellent Elementary Cellular Automata for context and a full description of the problem/simulation.

## Problem

NOTE: right now ppmtogif and display are only available on the solaris machines. If you would like to try out those programs (which is not required to do the assignment), log into nova.cs.berkeley.edu.

You are to implement a one-dimensional variant of Conway's Game of Life, heretofore called "Life 1D". Specifically, you will write the following program in C (from scratch) which supports the following:

UPDATE: the usage string we would like your program to print is:

```Usage: Life1D <rows> <rule>
```
We are including the older version here so you may reference the program behavior it describes.
```Usage: Life1D <rows> <rule>
This program simulates 1D Life: the simplest class of one-dimensional
cellular automata in a <ROWS=rows+1> x <COLS=2*rows+1> grid starting
with a single live cell in the middle of the top row using rule <rule>.
These 1D rules are defined in Wolfram's Elementary Cellular Automata:
http://mathworld.wolfram.com/ElementaryCellularAutomaton.html
This program will print to stdout data in plain PBM file format.
This output can be easily viewed using the display command or
converted to a another format using the pbmto* and ppmto* utilities.
A plain ascii PBM file can be created by adding a header line
"P1 <WIDTH> <HEIGHT>" and followed by a grid of data
(0 = dead = white, 1 = live = black).  Add a comment on the first
line with a brief description of the image.
Arguments:
<rows> is a positive integer specifying the number of rows to generate
(not counting the first "seed row" which is all dead except for a central
live cell). The columns are computed automatically -- enough so that
the rule, if it were to grow in the normal triangular pattern, would
just perfectly reach the edge. Off the board is considerered "dead".
<rule> is a number from 0-255 specifying the rule to use.
```
```  Examples:
See Rule 60 : http://mathworld.wolfram.com/Rule60.html
unix% Life1D 3 60
P1 7 4 ## 3 rows of Life1D (Rule 60) by Yourfirstname Yourlastname
0 0 0 1 0 0 0
0 0 0 1 1 0 0
0 0 0 1 0 1 0
0 0 0 1 1 1 1

See Rule 90 : http://mathworld.wolfram.com/Rule90.html
unix% Life1D 5 90
P1 11 6 ## 5 rows of Life1D (Rule 90) by Yourfirstname Yourlastname
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 1 0 0 0 0
0 0 0 1 0 0 0 1 0 0 0
0 0 1 0 1 0 1 0 1 0 0
0 1 0 0 0 0 0 0 0 1 0
1 0 1 0 0 0 0 0 1 0 1

See Rule 250 : http://mathworld.wolfram.com/Rule250.html
unix% Life1D 4 250
P1 9 5 ## 4 rows of Life1D (Rule 250) by Yourfirstname Yourlastname
0 0 0 0 1 0 0 0 0
0 0 0 1 0 1 0 0 0
0 0 1 0 1 0 1 0 0
0 1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0 1
```

## Assignment Correctness

The assumption that all cells off the grid are always considered "dead" causes will cause discrepancies in your results for certain rules when comparing your results to what you see at Mathworld. For example, your solution may generate this for rule 139:
```  \$ Life1D 17 139
P1 35 18 ## 17 rows of Life1D (Rule 139) by cs61c
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0
1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0
1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1
1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0
1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0
1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1
1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0
1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0
1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1
1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0
1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0
1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1
1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0
```
However, the images at Mathworld suggest that it should be like this:
```  \$ Life1D 17 139
P1 35 18 ## 17 rows of Life1D (Rule 139) by Mathworld
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
```
Can you spot the difference? The cs61c solution has several diagonals of zeros while the Mathworld solution does not. This is due to Mathworld assuming the grid is an infinite grid (versus a finite grid in this assignment). Therefore, for the sake of simplicity, the cs61c solution is considered the "correct" solution for this assignment. This means, you do not need to write additional C code to produce the Wolfram solution. For those of you who want to have a more "correct" solution, see the
Extra for Experts Section.

## Handling Error Cases

If the input doesn't satisful the constraints (i.e., rows or rule aren't valid integers in the specified range), you should print the Usage string above (just copy it into your code).

A great way to test your code is to run it through all the rules with 15 rows and check it against the catalogue of images on the bottom of the Elementary Cellular Automata page. You can generate a gif image by piping the output into ppmtogif and redirecting the output to a file. E.g.,
```unix% Life1D 3 60 | ppmtogif > Life1D_3_60.gif
```
Here are the gifs resulting from the examples above:

 Life1D 3 60 Life1D 5 90 Life1D 4 250

## Submission

Submit a single file Life1D.c by creating a directory called hw2 with your Life1D.c file in it. From within this directory run "submit hw2". Be certain that your program accepts command line arguments for <rows> and <rule>, and that you do not interactively prompt for these values. Otherwise, your program will hang and fail the autograder.

## Extra for Experts

If you want a "Wolfram" correct solution, add a new optional parameter named "Wolfram" to generate the correct result. For example:
```  % Life1D 17 139
;; would produce the cs61c solution
% Life1D 17 139 Wolfram
;; would produce the image that matches the website
```
If you really enjoy this project, you might want to consider implementing a
Totalistic Cellular Automaton, otherwise known as "Life1D in grayscale/color". Enjoy!

## Changes

• Usage string has been changed. We expect you to use the exact same string in your program.