gibson:teaching:fall-2012:math445:lab7
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gibson:teaching:fall-2012:math445:lab7 [2012/10/22 20:57] gibson created |
gibson:teaching:fall-2012:math445:lab7 [2012/10/31 19:34] (current) gibson |
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| - | **1.** Read Chapter 9 of the Moler text, and think through how the provided | + | **1.** Read [[http://www.mathworks.com/moler/exm/chapters/life.pdf|Chapter 12 of the Moler text]], |
| + | and think through how the provided | ||
| code updates the very first and last cells in the grid. What specific | code updates the very first and last cells in the grid. What specific | ||
| line or lines of code are responsible for these "boundary conditions"? | line or lines of code are responsible for these "boundary conditions"? | ||
| Line 10: | Line 11: | ||
| **2.** We are going to create our own code for the game of life and use a | **2.** We are going to create our own code for the game of life and use a | ||
| different approach based that does not allow anything to live on | different approach based that does not allow anything to live on | ||
| - | borders of the domain. We will let our board be 100x100 grid. Start a | + | borders of the domain. We will let our board be 50x50 grid. Start a |
| new script file, and start it with the lines | new script file, and start it with the lines | ||
| Line 36: | Line 37: | ||
| - | **4.** Initialize to zero a variable to count the discrete time ''t' and | + | **4.** Initialize to zero a variable to count the discrete time ''t'' and |
| then start a loop that stops after ''T'' iterations or when everything | then start a loop that stops after ''T'' iterations or when everything | ||
| - | is dead (Hint: what would ''max(max(L))'' return? What does the command | + | is dead (Hint: what would ''max(max(L))'' return?) What does the command |
| ''break'' do?). | ''break'' do?). | ||
| - | **5.** Implement the code given in Chapter 9 that will update the ''L'' matrix | + | **5.** Implement the code given in the Moler text that will update the ''L'' matrix |
| - | with periodic boundary conditions. Later we will change it to not be periodic. | + | with boundary conditions that repeat the border cells. Later we will change the |
| + | boundary conditions to enforce zeros on all boundaries. | ||
| **6.** In order to plot the figure, look up the function ''find'' in the help | **6.** In order to plot the figure, look up the function ''find'' in the help | ||
| Line 62: | Line 64: | ||
| your plots look better. If you use ''pause(0.5)'', Matlab will pause | your plots look better. If you use ''pause(0.5)'', Matlab will pause | ||
| just half a second, instead of waiting for you to hit return. | just half a second, instead of waiting for you to hit return. | ||
| + | |||
| + | **Better idea:** put the ''figure(1)'' command outside the for-loop, in the | ||
| + | initialization portion of your code. | ||
| **7.** You should now be able to run the code. If not debug it so that you | **7.** You should now be able to run the code. If not debug it so that you | ||
| - | can. Verify that the boundaries are periodic and wrap from one edge | + | can. |
| - | of the screen to the other. | + | |
| **8.** The following code will kill anything on a certain boundary | **8.** The following code will kill anything on a certain boundary | ||
| Line 87: | Line 91: | ||
| might be easier) is plotted and then ''hold off'' after the last point is | might be easier) is plotted and then ''hold off'' after the last point is | ||
| plotted. | plotted. | ||
| + | |||
| + | **Better idea**: Calculate four sparse matrices L1, L2, L3, L4, which are nonzero | ||
| + | wherever L is live and has 1, 2, 3, and 4 or more live neighbors, respectively. | ||
| + | Then plot all the nonzero entries of L1 with red, of L2 with blue, L3 with green, | ||
| + | and L4 with ''[0.5 0 0.5]''. | ||
| **10.** Change the orange color in the above plots to purple. What is the | **10.** Change the orange color in the above plots to purple. What is the | ||
| Line 106: | Line 115: | ||
| - | **14.** Turn in your completed code and the answers to the above questions. | + | **14.** (bonus) Modify your code to have periodic boundary conditions instead of zeros |
| + | on the borders. Does this change the long-term behavior of the system substantially? | ||
| + | **15.** Turn in your completed code and the answers to the above questions. | ||
gibson/teaching/fall-2012/math445/lab7.1350964664.txt.gz · Last modified: 2012/10/22 20:57 by gibson
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