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WOLFRAM|DEMONSTRATIONS PROJECT

Recurrence Table Attractors

​
x
n+1
function variables
a
0
b
0.7
c
1
d
0
e
0
f
0
y
n+1
function variables
g
-0.8
h
0
i
0
j
1
k
0
l
0
initial conditions
x
0.14
y
0.33
modulus
m
3
number of points
n
2000
randomize
x
n+1
0.7
x
n
+
y
n
y
n+1
2
x
n
-0.8
A recurrence equation such as
x
n+2
=
x
n+1
+
x
n
generates a sequence of terms based on an initial condition. For example, with
x
0
=
x
1
=1
, the Fibonacci sequence 1, 1, 2, 3, 5, 8, … is generated. A recurrence table can generate a multidimensional list of values. In this Demonstration, a range of two-variable recurrence equations is explored. When plotted, a variety of behaviors can be seen. The points may scatter randomly, or quickly converge to a set of values. About one time out of 50, a strange attractor is generated.
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