To prepare for this, I'll outline a little proposal.

Suppose you arrive at a peculiar town from the North and wish to travel South. There is just one street entering the town from this side. From then on, each street divides into two streets in the following PATTERN:

                                           N
                                           |
                                           |
                                           * 1 (path to *)
                                          / \
                                         /   \
                                        /     \
                                        |     |
                                      1 *     * 1 (paths to each *)
                                       / \   / \
                                      /   \ /   \
                                     /     |     \
                                     |     |     |
                                     |     |     |
                                   1 *   2 *   1 * (paths to each *)                                       / \   / \   / \
                                   /   \ /   \ /   \
                                  |     |     |     | 
                                  |     |     |     |
                                1 *   3 *   3 *   1 * (paths to each *)
                                 / \   / \   / \   / \
                                /   \ /   \ /   \ /   \
                                |    |     |     |     |
                                |    |     |     |     |
                              1 *  4 *   6 *   4 *   1 * (paths to ...)
                               / \  / \   / \   / \   / \
                              /   \/   \ /   \ /   \ /   \
                             |    |     |     |     |     |
                             |    |     |     |     |     |
                           1 *  5 *  10 *  10 *   5 *   1 * (paths ...)

                                        ETTSETTERY

A binomial pattern.