# Help

## Basics

Chaos - chaotic motion is explored in this program, and is shown to create fascinating patterns under some circumstances.

### Setting Up

First, set the step size to 0.01, then press 'Step'. What just happened? There are three target points on the canvas - two are blue, one is red.
The red one was randomly selected. The red X (henceforth called 'the X') just jumped 1% of the way towards that red target point (1% comes from the 0.01 step size),
and a new target point was selected (now highlighted in red.) Every time the X moves, it leaves a little black dot behind.

Press 'Step' a few more times and watch the X 'walk' around (this is called a 'random walk'.) Click 'Go ∞' to watch the random walk.

Now, check 'Quick Draw'. You can see that the walk stays pretty close to the center. As the X gets closer to one of the target points, there is a 33% chance that the X will move a small hop (1% of the way) towards the close target and a 66% chance that the X will make a larger hop towards the center (the sum of the probabilities of the other two points -- the hop is larger because the distance to each of those points is greater).

Press 'Step' a few more times and watch the X 'walk' around (this is called a 'random walk'.) Click 'Go ∞' to watch the random walk.

Now, check 'Quick Draw'. You can see that the walk stays pretty close to the center. As the X gets closer to one of the target points, there is a 33% chance that the X will move a small hop (1% of the way) towards the close target and a 66% chance that the X will make a larger hop towards the center (the sum of the probabilities of the other two points -- the hop is larger because the distance to each of those points is greater).

### Exploring

Click 'Reset' and change 'Step Size' to .1 (this is equal to 10%.) Repeat the above steps; watch the random walk when run to ∞.
Notice that the size of that cloud of points is bigger. That makes sense, each time it steps it's making
a bigger jump towards the randomly selected target.

First predict what will happen to the cloud of points, then run the following step sizes: .2, .3, and .5.

First predict what will happen to the cloud of points, then run the following step sizes: .2, .3, and .5.

### What?!

You should have noticed that a step size of .5 creates a special pattern: the Sierpinski Triangle.

Geometrically speaking, the Sierpinski triangle is gotten by taking a fully-shaded triangle, then connecting the midpoints of each side.

The resulting connected midpoints form a triangle inside the shaded one - delete all the area inside that middle triangle. That leaves three triangles,

one on the top and two on the bottom. Repeat this connect-midpoints-and-delete process for each. And then again for each of the 9 triangles etc.

See this link for a nice graphic.

Geometrically speaking, the Sierpinski triangle is gotten by taking a fully-shaded triangle, then connecting the midpoints of each side.

The resulting connected midpoints form a triangle inside the shaded one - delete all the area inside that middle triangle. That leaves three triangles,

one on the top and two on the bottom. Repeat this connect-midpoints-and-delete process for each. And then again for each of the 9 triangles etc.

See this link for a nice graphic.

### Ok, now what?

The best thing is to explore - check out other people's templates, make some of your own.

## Controls

- The best way to learn with this program is to explore! Here is a list of all of the Controls and what they do:
- Auto Place Targets/Custom - Switch between creating calculated targets (evenly spaced around a circle) or manually placing
- Number of Target Points - If target points are automatically generated, how many to make
- Scale - Change the proximity of the automatically placed target points
- Step Size - Jump size between current point and next target point as a ratio. A ratio between 1 and 2 allows points to be placed past the target (but not at infinity) - you may need to decrease the scale to see the entire picture.
- Iterations - How many points to calculate when you press Go!
- Quick Draw - Calculate infinite runs more quickly (by a lot)
- Display 'X' - Display the red X on the canvas and highlight the current target point
- Clear Targets - If set to 'custom', will remove all target points from the canvas
- Place Targets - Place target points on the canvas (inside the black box) by clicking
- Snap To Grid - Create a grid to which points will snap when manually added. You can change the grid size (default 100px).
- Go! - Iterate as many times as are input with Iterations
- Go to infinity - Iterate until a manual stop
- Stop run to infinity - Stop a run to infinity
- Reset - Remove points on the canvas (target points are unaffected)