This program does something like this well known animation (click to see it in action)

See also

Click to enlarge diagram

package twisted.loops;
/*
* Builds a mobius loop (a circular linked list). The loop is
* composed of several segments ("strips"). Each strip has two
* "sides." The "top" of a strip is attached top of the next,
* the "bottom" to the next's bottom. The last such attachment
* is "twisted" (top to bottom, bottom to top) so the loop has,
* effectively, only one side.
*/
public class Mobius {
    public static void main(String[] args) {
        Mobius mobius = new Mobius();
        Strip strip = mobius.create();
        Fly fly = mobius.new Fly();
        fly.land(strip.top);
        fly.escape();
    }
     /*
    * A loop segment with "two" sides
    */ 
    class Strip {
        Side top;
        Side bottom;
        String id;
        Strip(String id) {
            this.id = id;
            top = new Side(id + "-top");
            bottom = new Side(id + "-bottom");
        }
        public String toString() {
            return "Strip: " + id + ", " + ", top=" + top + ", bottom=" + bottom;
        }
         // Insert new strip/segment to loop 
        Strip attach(Strip strip) {
             // We point to new strip. New
            // strip points to next strip 
            swap(top.next, strip.top.next);
            swap(bottom.next, strip.bottom.next);
            return this;
        }
        void swap(Side a, Side b) {
            Side temp = a.next;
            a.next = b.next;
            b.next = temp;
        }
         // Twist a strip's connection to the next strip in the list.
        // Its "top" will point to the next one's "bottom"
        // and its "bottom" will point to the next one's "top"
        Strip twist() {
            Side temp = top.next;
            top.next = bottom.next;
            bottom.next = temp;
            return this;
        }
    }
     /*
     * One "side" of a strip (loop segment)
     */ 
    class Side {
        String id;
        Side next;
        public Side(String id) {
            this.id = id;
            next = this;
        }
        public String toString() {
            return "Side=" + id;
        }
        Side trap(Fly fly) {
            fly.land(this);
            return this;
        }
    }
    class Fly {
        Side legs;
        public Fly land(Side side) {
            legs = side;
            return this;
        }
        void crawl() {
            legs = legs.next;
        }
        void escape() {
            for (int count = 0; count < 25; count++) {
                System.out.println(this);
                crawl();
            }
        }
        public String toString() {
            return "Fly legs=" + legs;
        }
    }
     /*
     * Build a mobius loop (a circular linked list)
     * Uses method "chaining," see
     * http://en.wikipedia.org/wiki/Method_chaining
     */
    Strip create() {
        Strip strip = new Strip("A")
            .attach(new Strip("B"))
            .attach(new Strip("C"))
            .attach(new Strip("D"));
        strip.twist();
        return strip;
    }
    /*
     * Simple infinite loop
     */
    static void loop(int n) {
        for (int i=0; i < n; i = (i+1)%n) {
            System.out.println(i);
        } 
    }
}