fauxrealyo:

Time to search for grants! My kiddos NEED stand up desks. 

garp:

Knight’s tour

iomikron:

As you can see in this image (and others in previous posts) all these orbits are bounded in a region of phase space. Whereas some of them have an extremely complicated unfolding, this is taking place in a very specific region without escaping. The underlying concept of this concentration of states consisting the orbit (chaotic or not) is that of the attractor.

The attractor is part of the phase-space of a dynamical system, where its orbits converge. It can be a point (or points), a limit cycle, a surface, or a volume.

Except from these cases, attractors may be much more complicated, like the one of the figure above. These complex types of attractor are called strange attractors. In strange attractors the concentration of orbits can be very dense, and their mathematical description requires the definition of a more generalized concept of dimension.

Thus, the above structure, due to its complexity, corresponds to a strange attractor.

Rendered with chaoscope

matthen:

If you roll a circle inside one 3 times its size, it will actually trace out a 4 pointed star shape called an Astroid (this shape is traced out in the animation in orange).  But what if inside the smaller circle, there is an even smaller one tracing out a smaller Astroid?  This animation shows the intricate shape that is generated by adding the effects of all the Astroids.  [code] [also]

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.