Perpetual Braid (Fractal tiling)

A decorative dendritic fractal tessellation

Art

Creative Commons Attribution Noncommercial Share Alike

Commercial use is not allowed, you must attribute the creator, you may remix this work and the remixed work should be made available under this license.

Learn more or download attribution tags

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:

https://archive.bridgesmathart.org/2020/bridges2020-49.pdf
https://web.archive.org/web/20210814135748/https://archive.bridgesmathart.org/2020/bridges2020-49.pdf

Materials and methods

PLA

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.

Documents

Issues

Issues are used to track todos, bugs or requests. To get started, you could create an issue.

Comments

Mini bubblevoidbubble published this design ago