aperiodic bikini reptiles

this looks very different from the helices but it is a related exercise in tiling, in this case it is aperiodic.

the bikini reptiles will tile periodically in repeating patterns but if some simple rules* are applied they will tile an infinite plane in a non periodic (aperiodic) manner with no discernible repeating pattern.

the simplest rule is that 6 shield shapes cannot be allowed to meet at one point and that voids cannot be allowed to form.

the actual pattern is dependent on fine tuning the mix between shields and bikini's.

*the need for joining rules to achieve an aperiodic pattern is necessary for all types of aperiodic tiling including Penrose tiles, kites and darts and rombs, to prevent a periodic tile layout being generated.

 the tiles are set out on a hexagonal grid and can tile an infinite plane aperiodically

 this red blue tile pattern may look very different from the bikini reptiles but it is fundamentally the same aperiodic tiles.  the only difference is that the joining condition is represented by a either a sharp projection or an incision rather than convex and concave edges.  the same joining rules apply whereby 6 red tiles cannot be allowed to meet at one point.