Project 4 — 1D Cellular Automata

Simulator Source Code and Executable

CASimulator.java (source code)
CASimulator.class (executable)

This program was written in Java by a student who took the class in Fall 2007. It automates the entire process of the table walkthroughs, calculating and recording the parameter values, and generating images of the CAs. In Fall 2009, a student modified the program to make gathering the data and classifying the images easier.

Running the program

To run the program, type the following at the command line: 

java CASimulator X
where X is the number of experiments to run.

Note for 527 students: In order to compute the fifth parameter, you may need to modify the given Java program. The program has a place holder for this in the function calculateZeta(). The fifth parameter is declared as a variable of type double named zeta. It is generally better to come up with a new parameter that implements a different way of examining the states and neighborhoods, rather than simply taking averages of the given parameters.

Experiment records

The program will create an experiment record sheet in .csv format for each walk-through (experiment). The experiment records for all the experiments are included in one master .csv file called MasterExperiment.csv. The 4 lambda and entropy values are automatically written to these reports, as well as the zeta value for the 5th parameter. You will need to fill in your name, the class for each step of each walk-through, and an observation for each step of each walk-through. You may also need to adjust the width of some of the columns. When filling in the class for each step of each walk-through, enter "0" for classes I and II, "1" for class IV, and "2" for class III. This will facilitate making the graphs with the class numbers. When filling in the observations column, the more steps that you include an observation for, the better. Including observations for every step (or nearly every step) may boost your grade slightly. You are required to do at least 20 experiments. Doing more than 20 can earn you a higher grade.

Images of CAs

The program will also generate a .jpg image for each step of each walk-through. You will examine these images to fill in the rest of the information in the record sheets, namely, the class and the observation. Each experiment has a separate directory which includes all the generated .jpg images for that experiment. Each of the experiment directories are included in the master directory Experiments. Also, the program will generate an .html web page for each experiment which will show all .jpg images for that experiment side by side to make viewing and classifying the images easier.

Classification of the CAs

A significant piece of this project is to view images and make a classification based on what you observe. This can be somewhat challenging since it is very subjective. The link below provides several examples from each of the 4 classes to help guide you in this process.

Classification of 1D Cellular Automata

Note that it is relatively rare to get class IV behavior, so don't worry if you don't end up with very many instances of class IV.

Calculations

Compute the average and standard deviation of each of the 4 parameters (also the 5th parameter for 527 students) for each instance among all walk-throughs that you classify as Class IV. Be sure to state which of the 4 parameters appears to be the best indicator of Class IV, and explain why. To get these calculations, it is probably best to copy all of the Class IV instances into another spreadsheet (or at the bottom after all the experiments) so that they are all together. This will make it easier to define the average and standard deviation formulas. For the average, you can use the formula =average(begin:end) and for the standard deviation, you can use the formula =stdev(begin:end), where begin and end are the cells that the data begins and ends at, respectively. For each parameter, the begin and end column will be the same, and the row number will be different. Use these formulas for each of the parameters.

Graphs

Make a graph for each of the 4 parameters (527 students will also make a graph for their 5th parameter). On the x axis is the value of the parameter, and on the y axis is the classification. It may help to include two versions of each graph: one that has all the curves, and one that just has the points. Including 20 or more curves on one graph can get a bit messy, so making an additional graph with just points can be helpful. Here is an example of what the graphs might look like for lambda (for 40 experiments):



These graphs were made using Excel. Below is an explanation for how to create graphs like these for both 2003 and 2007 versions of Excel. If you prefer, you can also use other graphing utilities, such as GnuPlot or MatLab.

Excel 2003

To add a graph, choose "Chart" under the "Insert" menu. The "Chart Type" window appears first. Choose "XY scatter plot", then the type of scatter plot (points or curves) on the right. Then click the "Next" button. The "Source Data" window appears next. Choose the "Series" tab to define the plots. After clicking the "Add" button, you can define the X and Y values for the series. The X values will be the parameter value (e.g. lambda), and the Y values will be the class number. To define these values, you can just go to the corresponding column in the spreadsheet for the series (experiment) you are on, and highlight the 13 rows in that column that have the parameter values or class numbers. After you release the mouse button, the formula will then appear in the box for the X values or the Y values. Repeat this process for each of the 20 (or more) experiments. You will have a series for each experiment. When you have defined all of the series, click the "Next" button. The "Chart Options" window appears next, and here you can include titles for the chart and the X and Y axes. Choosing the "Finish" button will insert the chart as you defined it into the spreadsheet. After the chart is inserted, you can right click on it to change anything in the "Chart Type", "Source Data", or "Chart Options" windows.

Excel 2007

First, click on a blank cell of the spreadsheet so that you will start with a blank graph. Then from the "Insert" menu tab, choose "Scatter" under "Charts", and then choose the type of chart you want from the dropdown menu (points or curves). A blank chart will now appear in the spreadsheet. Then click on "Select Data" from the "Data" tab in the menu area. Here, you can add the series of plots. You will have a series for each experiment. Click on the "Add" button, and this will pop up a window where you can add the X and Y values for the series. The X values will be the parameter value (e.g. lambda), and the Y values will be the class number. To define these values, you can just go to the corresponding column in the spreadsheet for the series (experiment) you are on, and highlight the 13 rows in that column that have the parameter values or class numbers. After you release the mouse button, the formula will then appear in the box for the X values or the Y values. When you have entered formulas for both X and Y, the plot will appear in the graph. Repeat this process for each of the 20 (or more) experiments. To include labels for the chart and the axes, choose the "Layout" tab under "Chart Tools" in the menu above. Use the options "Chart Title" and "Axis Titles" in the "Labels" section in the menu to add the labels.

Discussion

Discuss the correlations (if any) between the parameter values and the class behavior. Indicate the general range of values associated with Class IV behavior. Be sure to point out any anomalies and give possible explanations for these anomalies. Note if you've observed Class I or II behavior at high parameter values, or Class IV or III behavior at low parameter values. The more discussion and analysis that you do, the higher grade you can earn.

There is no required length of the report, and quality is generally more important than quantity. As a general guide for this project, a couple good sized paragraphs should be enough to satisfy the basic requirements. Of course, you will likely need to include more discussion than that to get a higher grade.

Submission

Submit the following items:

Note: While it is a good idea to include a few images in your report as part of your discussion, it is not necessary to submit all your images that were generated. You will have over 200 images, and this can result in large submission file sizes, so it's best not to include them.

Submitting your work

Tar or zip your files together and send them to the TA. The directory should include your report (in .pdf) and the .csv or .xls experiment sheet.

Grading:

Earning higher grades:

As with all the projects this semester, fulfilling the basic requirements will earn you a B. To earn higher grades, you will need to do further experimentation and/or further discussion/analysis. For this project, if you do significantly more walk-throughs (eg. 30 or 40), that would boost your grade to a B+. If you also do well on the report and include thorough analysis, that would boost your grade to an A. If a 420 student does the 527 portion, that will earn at least an extra half letter grade, possibly a full letter grade.

Avoiding lower grades:

Your grade will lower from a B if you fail to perform some of the required experiments and/or you do a poor job on the report. If you did only 10 experiments (instead of 20), that would probably lower your grade by half a letter grade. Not including a discussion would probably drop your grade by a full letter grade. For example, if you just did 20 experiments, but turned in no report, no graphs, and no calculations, assuming you fulfilled the classification work for the 20 experiments, your grade would probably be a D. Avoid this by doing and submitting all the required items!