Warning: unfortunately, this is very slow to load, and somewhat slow to run. Please wait. Written for / tested with Chrome on mac.

This is to illustrate something about the boundary of the Heighway fractal dragon and relatives. There are a number of imperfections, but hopefully this is adequate for explaining some of the ideas about these curves and boundaries.
This is based on the result in my preprint https://arxiv.org/abs/2402.16106. This is inspired by the work of S. Tabachnikov. Dragon Curves Revisited, Math. Intelligencer, vol. 36, no. 1, 2014, pp. 13--17. Michel Dekking, Paperfolding morphisms, planefilling curves, and fractal tiles, Theoretical Computer Science, vol. 414, no. 1, pp. 20–37, (January-2012). , J. Arndt and J. Handl, Edge-covering plane-filling curves on grid colorings: a pedestrian approach.
Another program which shows the boundary of other folding curves can be found here. Note that that version uses the L-system in the code to produce the boundary as an svg file, whereas this program uses the matrices of the IFS to produce the image. The basic version of this program can be found here, which runs fairly quickly. Unfortunately the added extras for this version have not been tacked on particuarly carefully, so this is very slow; rewriting on the to do list.

A couple of notes on the image (other notes appear when clicking preset buttons): Two little black dots are at either end of a partcular segment iterate for reference. Other dots are for controls of colour etc; may only work on chrome on mac, not widely tested. Turn off dots with dots button. The controls are over the image initially, but you can click the controls button to make them disappear, or go before the image, i.e., not overlap.
Notes on controls: Most notes appear in the controls section when you click on the variation radio button. in variation 1, yellow dot controls appearance. y <0.9 (yellow dot near bottom of screen) means coloured paths, otherwise red and blue. Arrows shown in variation 1. 0.9 <y <0.8: only two central initial segements shown
Background options: white background; black/white checkerboard background;
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