**Program 1:** "Binary dice"

This program is a simplified version of the program used for the simulations described in Chapter 4. Here, you choose the number of dice and the number of steps. The program starts with an all-zero configuration. At each step the program chooses a dice (either at random or sequentially) then flips it to get either “zero” or “one” with probability . The program records the sum of the dots on all the dice, and plots the sum as a function of the number of steps. It is suggested that you start with a small number of dice; 4, 8, 10, 20 and then go to 100 and 200. If you have a fast-working computer, you can go up to 1000 dice and 2000 steps. This will take some time but it is rewarding. Check both the random and the sequential options. Follow the changes in the curve when you increase the number of dice. Examine the smoothness of the curve, the number of steps to reach the equilibrium line, and the number of times the sum goes back to zero. Have fun and good luck.

**Program 2:** "Regular dice"

This program does the same as program 1 but uses regular dice with outcomes 1,2,3,4,5,6. You can play with this program if you feel more comfortable with the conventional dice. It does not add anything new to what you can learn from program 1.

**Program 3:** "Card Deck"

This program is essentially the same as program 1 but makes use of cards (or if you like dice having 13 outcomes 1,2,…13). You can play with this program if you prefer to look at cards, instead of dice. Again, you would not gain anything new with this game. Enjoy yourself.

**Program 4:** "Simulation of
expansion of ideal gas"

The program is essentially equivalent to program 1. However, instead of dice, you start with N dots, each dot representing a particle. Instead of two outcomes {0,1}you have the two outcomes {L,R}, L and R stand for being in the left or the right compartment. The equivalence of the two processes is described in Chapter 7. The program chooses a particle at random, then chooses either R or L at random and place the particle in either the R or L compartment, respectively. The graph follows the total number of particles in the left compartment from the initial to the equilibrium state. This is essentially a simulation of an expansion of an ideal gas.

**Program 5:** "Simulation of
mixing two ideal gases"

This is essentially the same as program 4, but with two sets of particles. The blue dots expand from the left (L) compartment to the entire volume, and the red dots expand from the right (R) compartment to the entire volume. This is often referred to as a “mixing process”, but it is basically an expansion of two different gases. Again, this program does not add any new idea that is not contained in the expansion process simulated in program 4.

**Program 6:** "Find the
hidden coin"

This is a very important game to learn what “missing information” means. You can see the difference between the “smart” and the “dumb” strategy as discussed in Chapter 2. You choose the number of boxes N. The program chooses a number between 1 to N at random, say K, and hides a coin in the box numbered K. You can see where the coin is, by clicking the “reveal coin” button, but I do not recommend that you do so until after you play the game. Click on “start” and ask where the coin is. You can either select single boxes like {1,7,20…}, or a range of boxes like {1-30, 30-70}. The program answers you with either a YES or a NO. You keep on asking binary questions until you find where the coin is hidden. Examine how the total number of questions changes according to the “strategy” you choose for asking questions (see also Chapter 2 for more details).

**Program 7:** "Generating
the Normal distribution"

In this program you can generate the normal distributions that are discussed in Chapters 3 and 7. You throw n dice at random. The program calculates the sum of the outcomes and records how many times each sum has appeared. The frequencies of occurrence of each sum, is then plotted as a function of the sum. Start with 2 and 4 dice and see how the frequencies as a function of the sum changes when the number of dice increases to 16 and 32. For larger number of dice, see Figures 3.7 and 3.8.