Fibonacci tiles

thingiverse

This generates a Fibonacci tile - see Christoffel and Fibonacci Tiles Alexandre Blondin-Masse, Srecko Brlek, Ariane Garon, and Sebastien Labb https://link.springer.com/content/pdf/10.1007%2F978-3-642-04397-0_7.pdf These tiles seamlessly interlock to form a cohesive pattern. The inset parameter precisely adjusts the tile's dimensions to determine the optimal interference in a 3D print or (negatively) the exact offset required for laser cutting. The Wikipedia article https://en.wikipedia.org/wiki/Fibonacci_word_fractal makes a compelling claim that there is a gap in the tessellation, but upon closer inspection, it becomes clear that this is not the case. A revised version of the tile has been added, correcting an earlier oversight. This updated design is now known as the Fibonacci snowflake and it successfully tiles the plane without any gaps or overlaps. 2019-03-17 - An additional order was overlooked, but it has since been incorporated into the design. The accompanying images are generated from another OpenSCAD script that expertly handles the tessellation process. 2019-03-17 issue with offsetting tiles resolved.