A closed meander of order 120: a closed curve that intersects a line at 120 points, without intersecting itself.

Conchoids of a 5 cusped epicycloid with pole at center.

Boundary formed by trochoids of different parameters.

Parallels of the Witch of Agnesi by Xah Lee

Above are hypocycloids, curves produced by fixing a point on the circumference of a small circle of radius b, rolling around the inside of a large circle of radius a > b. If a/b is rational, i.e. it can be expressed as a fraction, the path will return to it's starting point. If the ratio is irrational, the path will never touch the same spot on the circumference of the larger circle more than once, and images such as the ones above result.

A rhumb line (or loxodrome) runs from the north to the south pole passing through the intersections of the longitude and meridian at the same angle every time.

"Koch Curve 85degrees: Generalizing the von Koch curve with an angle a chosen between 0 and 90°. The fractal dimension is then


http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

The construction of Hilbert's space-filling-curve.