Play around with the 2D chaos game

Write your own code to calculate where the next point should be. The default code simply picks one of the vertices at random and moves the current point halfway there. But you can change that using functions, operators, and whatever else you can find in MathJS. You can use the coordinates of the current point, currentPoint, and the coordinates of each target vertex, targetPoints. Both are matrices. All you must do is set the nextPoint variable to either an array of two numbers like [100, 200] or a matrix like [[100, 200]].
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userControl() function Create a custom UI control. Example: t = userControl("some number", -1, 4, 3) will create a slider ranging over -1 to 4 and starting at 3. You can then use t anywhere in your code to give your end user 'live' control over something.
write() function Use this function to output text to the console. Example: write(currentPoint)
Technique: saving data for the next iteration Variables set in one iteration are available in subsequent iterations. See "Avoid previous target vertex" in the advanced examples, below.
Optional initialization code When the "Show advanced" checkbox is checked, another code window is visible. This is for code that you want to run only once, before the first point is created.

The following functions are usually used in the optional initialization code:

vertices(), points(), and opacity() functions Set the fields seen above, programmatically. Example: vertices(5) will set the Vertices field to 5.
zoom() and pan() functions Set the zoom level or center of view fields (see below) programmatically.

Show advanced examples

Advanced example - The Levy C curve fractal:

zoom(325)
A = matrix([[.5,  .5], [-.5, .5]])
B = matrix([[.5, -.5], [ .5, .5]])
point1 = transpose(multiply(A, transpose(currentPoint)))
point2 = transpose(multiply(B, transpose(currentPoint)) - transpose(matrix([[.5, .5]])))
nextPoint = randomInt() ? point1 : point2

Advanced example - Avoid previous target vertex:

# IMPORTANT! Put these two lines in the "Optional initialization code" pane.
previous_vertex = -1  # start with a non-existing vertex
slider = userControl("how far to go toward the target", -2, 1.4, .5)

# The rest of this code goes in the main pane

# Get all possible indices except the vertex we used in the last iteration
_possibleTargetIndices = math.range(1, targetPointsLength+1)
_possibleTargetIndices = _possibleTargetIndices[_possibleTargetIndices != previous_vertex]

# Pick a random target vertex
_nextTargetIndex = math.pickRandom(_possibleTargetIndices)
# ... and get its coordinates
_nextTarget = targetPoints[_nextTargetIndex, :]

# Make next point midway to the target
nextPoint = (currentPoint + _nextTarget) * slider

# Store current vertex for next iteration
previous_vertex = _nextTargetIndex

Advanced example - The Corcoran Attractor:

# try sine_scale of 1/3 and 12 vertices with a 3 million points and 0.1 opacity!
nextTargetIndex = math.randomInt(1, targetPointsLength+1)
_nextTarget = targetPoints[nextTargetIndex, :]

# Create user controls for the parameters
sine_shift = userControl("Sine shift", 0, 2*math.pi, math.pi*29/25)
sine_scale = userControl("Sine scale", -3/2, 4, 1/2)
sine_offset = userControl("Sine offset", -1, 7/4, 1/2)

displacement_factors = math.matrix([
  [math.sin(_nextTarget[1,2] + sine_shift) * sine_scale + sine_offset,
   math.sin(_nextTarget[1,1] + sine_shift) * sine_scale + sine_offset]
])
# Apply the factors to the displacement
displacement_to_target = _nextTarget - currentPoint
nextPoint = currentPoint + math.dotMultiply(displacement_to_target, displacement_factors)

Optional initialization code (runs once before first iteration):

Examples:

Add 1 to both x and y:

nextPoint = currentPoint + 1

With rotation:

nextTargetIndex = math.randomInt(1, targetPointsLength+1)
_nextTarget = targetPoints[nextTargetIndex, :]
midpoint = (currentPoint + _nextTarget) / 2
rotation = [[math.cos(math.pi/4), -math.sin(math.pi/4)], [math.sin(math.pi/4), math.cos(math.pi/4)]]
nextPoint = math.multiply(midpoint, rotation)

Play around with the Chaos game!

Examples: