Very cool. I have been trying to do something similar with tilings, but there is more information to be encoded. I am targeting something similar to the ability to render the tessellation catalog [1] and perform searches. Turns out there are multiple notations, and most of them use some level of implied knowledge. Also seems like rendering of knots is more open ended, while tilings are essentially their rendering. But they all do use a similar approach of Notation > Half Edge Data Structure > Render.<p>[1] <a href="https://zenorogue.github.io/tes-catalog/?c=" rel="nofollow">https://zenorogue.github.io/tes-catalog/?c=</a>
There's some fun stuff here (I'm reminded of the algorithms used to render planar drawings of proteins, which are similar to knots).<p>My real interest which I haven't seen much literature about is generating real-world knots that have good properties. For example if you look at the various knots, some knots have nice properties like "easy to untie" and "does not get tighter under load", which has huge impacts. These properties derive from the topology but also the physics of the knot. Would be nice to find a new hitch knot that worked better.
Neat visualization. I noticed though that the images (when enlarged) have some awkward angles etc to them, they are not super rounded and smooth shapes... maybe the width modulation could use some easing or interpolation or something?
As a knotable person myself, this is AMAZING.<p>Some thoughts on application of this knowledge would be to look at the patterns as you have described as cross-sections of rope weaving with the circular looming as the individual bobbins/spinny-things in an industrial loom - so rather that just woven-sheeth and full spin style cabling, one might achieve some really incredible properties in the woven elements along a axis such as these represent.<p>Especially if you further differentiate btwn material and woven state (Are you weaving in an already spun set of filiments? What are the materials for the various inputs, and even further - imagine you have a set of elements in the loom where youre certain threads are the static, more rigid scaffold - like woven titanium strands which then feed into another loom which is weaving in the kevlar or other materials including a core of optics which is protected by the outer woven sheath from these patterns of 2D knots stretched out along an axis - certain elements can be printed such like the articulating spine of a snake.<p>It could make a machinable-high-tensile strength cable with an optical core with protected turn radii (titanium snake spine)<p>See here for reference to advanced cabling:<p><a href="https://www.youtube.com/watch?v=AD5aAd8Oy84" rel="nofollow">https://www.youtube.com/watch?v=AD5aAd8Oy84</a>
Love the double hearts in <a href="https://prideout.net/blog/svg_knots/knots/8_5.svg" rel="nofollow">https://prideout.net/blog/svg_knots/knots/8_5.svg</a>
How is it feasible to have a .svg file that has links to other .SVG files? <a href="https://prideout.net/blog/svg_knots/knottable_v1.svg" rel="nofollow">https://prideout.net/blog/svg_knots/knottable_v1.svg</a>. Has this capacity been around for some time?