Cobweb plotter
Date: 12 February 2013

This applet performs cobwebbing for a first-order difference equation
[math]x_{n+1} = f(x_n)[\math]

Enter the function [math]f(x)[/math] in the box, and choose an initial condition [math]x_0[/math] by dragging the point on the x-axis or typing a value in the textbox.

Click 'Iterate' to perform the next step in the cobwebbing.

Zoom in and out using the zoom buttons, and click & drag on an empty part of the screen to move the view.

n

g(x)=

x_0=

Step

x_{0}

Show details

Iterate

x_n

Reset

a = 3.47 (slider from 0 to 4, step 0.01)
s = -2 (slider from -5 to 5, step 1)
h = 0.1
f(x) = ((a * x) * (1 - x))
x0 = 0.7113226084176667
n = 82 (slider from 1 to 100, step 1)
list1 = IterationList(f, x0, n)
steppart: 1
nR = If(steppart ≟ 0, n, n - 1)
A2 = 0
B2: x0
fInputBox = Textfield(f)
x0InputBox = Textfield(x0)
oncurves = Sequence((Element[list1, i], Element[list1, i + 1]), i, 1, n)
diagonals = Sequence((Element[list1, i], Element[list1, i]), i, 2, nR + 1)
initialized: true
vertsegs = Sequence(Segment[Element[diagonals, i - 1], Element[oncurves, i]], i, 2, n)
Q: (0, Element[list1, n + 1])
R: (Element[list1, nR + 1], 0)
activehorizontal = Segment(Q, (x(R), y(Q)))
activevertical = Segment(R, (x(R), y(Q)))
horizlong = Sequence(Segment[Element[oncurves, i], (0, y(Element[oncurves, i]))], i, 1, n)
vertlong = Sequence(Segment[(x(Element[oncurves, i]), 0), Element[oncurves, i]], i, 2, n)
X_{0} = Point(xAxis)
initialvert = Segment(X_{0}, (x0, f(x0)))
text1: "x_{" + n + "}"
text2: "x_{" + nR + "}"
details = false
horizsegs = Sequence(Segment[Element[oncurves, i], Element[diagonals, i]], i, 1, nR + 1)
A3 = 1 (slider from -5 to 5)
B3 = Element(list1, 2)
A96 = 94 (slider from -5 to 100)
B96 = Element(list1, 95)
A97 = 95 (slider from -5 to 100)
B97 = Element(list1, 96)
A98 = 96 (slider from -5 to 100)
B98 = Element(list1, 97)
A99 = 97 (slider from -5 to 100)
B99 = Element(list1, 98)
A100 = 98 (slider from -5 to 100)
B100 = Element(list1, 99)
A101 = 99 (slider from -5 to 100)
B101 = Element(list1, 100)
A102 = 100 (slider from -5 to 200)
B102 = Element(list1, 101)
A44: 42
B44 = Element(list1, 43)