WOLFRAM|DEMONSTRATIONS PROJECT

Spiral Explorer

​
a
b
connect points
show axes
In his book Spirals: From Theodorus to Chaos, Philip J. Davis explores the recurrence relation
z
n+1
=a
z
n
+b
z
n
/
z
n

, where
a
and
b
are complex numbers. If you set
a=1
and
b=
with
z
0
=1
,
​
then you obtain what Davis refers to as the 'discrete' version of the spiral of Theodorus. By varying the values of
a
and
b
it is possible to obtain a wide variety of different spiral-like structures.