Some Maple animations

### Some Maple animations

Maple's `plots` package has an animation feature. For example, try

```with(plots):
animate(sin(x*t), x=-Pi..Pi, t=-5..5);
```

Click on the plot to select it, and then choose the Play option on the Animation controls to see the movie. (There is an Animation menu on the main menu bar; also you can enable the Context Bar on the View menu, and then pictorial controls will appear in the context bar when you select the animated plot.)

It is also possible to create a movie "by hand" by splicing together a sequence of plots. For example, the following code mimics a screen saver that bounces a geometric figure around the screen.

Warning. Before you try this example, save your work and close any unneeded windows. Since this example uses a lot of colors and demands a lot of Maple's memory, it could possibly crash your Maple session. (If that happens, try again with the number of iterations set to `i=1..10` instead of `i=1..100`.)

```r1:=rand(-10..10):  r2:=0.2*rand(6):
p:=seq(plots[polygonplot]([[r1(),r1()],[r1(),r1()],[r1(),r1()]],
color=COLOR(RGB, r2(), r2(), r2() ) ), i=1..100):
plots[display]([p], insequence=true, axes=none,
title="Moving Triangles", titlefont=[TIMES,BOLD,72]);
```

If you cut and paste this code into a Maple session and execute it, you should get a plot that looks something like the figure. When you start the animation playing, you should see randomly colored triangles move around the window.

Explanation: Maple's `rand` command is a pseudo-random number generator. The command `rand(-10..10)` defines a procedure to generate a random integer between -10 and 10, so the `polygonplot` command above makes a triangle whose vertices are at random integral points within a 20 by 20 square. The command `rand(6)` defines a procedure to generate a random integer between 0 and 5 inclusive, so the color instruction above generates a color with a random mixture of Red, Green, and Blue in the standard 216-node color cube. The whole procedure generates a sequence of 100 randomly placed triangles with random colors, and the `insequence=true` command produces the animation.

Exercise

Reproduce the Math 696 logo by using a Maple animation.