The TI-92 material for this module has two parts. This part discusses modeling diffusion using simulations. The other part discusses modeling diffusion using Markov chains. Click here to go to the section on modeling by Markov chains.
The TI-92 function rand() can be used as the basis for simulations like the one in the Java applet. This function produces a random number between zero and one -- possibly zero but never one. The TI-92 screen below shows some examples. Try it yourself.
Now suppose that we want to simulate a molecule in one of the end, or outer, cells in our five-celled organism. Recall that in each unit of time or in each "tick of the clock" the molecule stays put with probability 75% and jumps to the adjacent cell with probability 25%. The TI-92 function below, outrcell, simulates this.
The TI-92 screen below simulates several "ticks" of the clock.
The TI-92 function below, tick is more complicated and simulates what a molecule in any one of the five cells does in one "tick of the clock." That is, if you execute tick(n) where n is 1, 2, 3, 4, or 5 the function determines probabilistically where a molecule in cell n will be after one tick of the clock. You can obtain this program in the usual ways -- by downloading it using a TI-Graph Link cable, by obtaining it from another TI-92 using the linking cable, or as a last resort, by typing it in.
Explain how the function tick works.
The TI-92 screen below illustrates how the function tick can be used.
You can use this function together with the usual tools for working with sequences to look at some examples of the travels of a molecule as it moves around the organism. The TI-92 screens below show two examples for a molecule starting in the middle cell.
These graphs were produced by setting the TI-92 Graphics mode to SEQUENCE and the Y= and WINDOW screens as shown below.
The TI-92 screens below show two examples for a molecule starting in the rightmost cell.
The TI-92 program below runs simulations like the ones described in the narrative part of this module. Executing ticksim(n) from the home screen simulates 100 ticks of the clock for n molecules. All the molecules start in the middle cell.
The TI-92 screens below show the starting situation and the situation after one tick of the clock with 200 molecules.
You can use the ideas developed here and in the laboratory material on Markov chains to study questions like the ones raised in the narrative part of this module.
