Perpetual Braid (Fractal tiling)
Description
_With a furtive start, the placement of a single tile, a winding cascade ravels the motif into the infinite._ This tile is designed using Robert W. Fathauer’s method for creating monohedral tilings, with branching tiles exhibiting a fractal boundary. Its outline is a fudgeflake fractal with symmetrical cutouts. The tile decoration is inspired by a japanese weave pattern and can be printed in multiple colours by making colour changes at the appropriate height(s). It is meant for printing with two perimeters, without any top or bottom layers, and zero infill. A selection of colours, tiling patterns and paths, and an option of tiles with or without a weave, brings endless possibilities to your work of art. You can find more information on dendritic fractal tile design here: [A Method for Creating Dendritic Fractal Tiles](https://archive.bridgesmathart.org/2020/bridges2020-49.pdf) [A Method for Creating Dendritic Fractal Tiles - archived](https://web.archive.org/web/20210814135748/https://archive.bridgesmathart.org/2020/bridges2020-49.pdf) __Instructions__ Bottom part (0-2.2 mm): - Layer height: 0.2 mm Weave pattern (2.2 - 3 mm): - Line width: 0.45 mm - Layer height: 0.2 mm - Bottom layers: 0 - Top layers: 0 - Infill: 0% - Walls / perimeters: 2 To print the tile in 2 colours, issue a colour change at the 2.40 mm mark. To print it in 3 colours, issue an additional colour change at the 2.80 mm mark. Project files with the settings above are provided.
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