Circle Limit III

This is an animation of Escher's woodcut print, Circle Limit III.

The original print is a hyperbolic tessellation projected onto the Poincare disc with the centre of the projection where the right fin tips of yellow and green fish meet. This animation moves the centre along a straight line starting from this point, passing through several points of interest: the meeting of three noses and three tails, the left fin tip of three fish, the right fin tips of red and blue fish, and then the same points again before coming back to yellow/green fish.

Visually, the pattern almost seems like it could be moving along the surface of a pringles potato chip. The pattern being hyperbolic can be seen by noting that the very top and bottom of this circle move to the right at twice the speed of the centre. A spherical pattern projected to the same circle would be stationary at the top and bottom, while a planar pattern would move at the same speed at the top and bottom as in the middle.

The motion of the animation is unrelated to the pattern of the fish and unfortunately seems take some of life out of it. Fish of the same colour lie along curves of 'through traffic', shooting up from the distance of the boundary and falling off again to the boundary elsewhere. The flow of fish along these curves is overwhelmed by the animation, locking the mesh of fish together moving them with no regard to where they otherwise would be going.

This animation was made using ghostscript and ffmpeg.

Category:

Education

Tags:

• escher
• circle
• limit
• hyperbolic
• tesesllation
• poincare
• disc