Ellipses

Ellipses (Christian Wolinski)

Construction :

Place :
1. Connectors
2. Chambers

To satisfy following :

There are any number of connectors.
Connectors are vertical and connect every chamber they intersect.
Connectors pose no restrictions inside chambers.

There are exactly K chambers on levels 0 thru M.
Every pair of chambers does not intersect.
Every chamber is a horizontal ellipse of any orientation, eccentricity, size.
Every chamber has at least 1 and at most 3 connectors.

Traversal :

Traversal path consists of exactly N directed straight line segments.
A path begins in chamber 1, connector 1, at point A=[1,0,0] and ends in chamber 2, connector 2, at point B=[-1,0,0]
Every segment of a path is contained in one chamber.
Every endpoint of a segment lies either on a connector or on a chamber's boundary.
If a segment ends on a connector then the next segment must originate with this connector.
If a segment ends on a chamber boundary the next segment must follow a reflection.

Score equals the log of the number of distinct traversal paths.
Please send us a simpler description.