Orbits of the Gingerbreadman Map

parameter λ

0

⊕

hide all locators

We introduce a parameter

λ

in the classical two-dimensional gingerbreadman map,

x

k+1

=|

x

k

|-(1-λ/5000)

y

k

+1

,

y

k+1

=

x

k

,

k=1,2,…

.

Orbits are generated by iterating the map 3000 times using different initial points. Six orbits are plotted initially, starting from six different initial points marked by the locator objects "

⊕

".

You can drag these initial points or add and/or delete new ones (Alt+Click on Windows) inside the plot.

Each orbit is colored differently and the colors are repeated cyclically every six orbits.

External Links

Gingerbreadman Map (Wolfram MathWorld)

Permanent Citation

Erik Mahieu

"Orbits of the Gingerbreadman Map"
http://demonstrations.wolfram.com/OrbitsOfTheGingerbreadmanMap/
Wolfram Demonstrations Project
Published: March 7, 2011