The 8.8 knot

Variation on the 8.8 knot in honor of Dunkel, et al. the MIT team who demonstrated knots various strength according to a clever color changing fiber scheme.

Basically, a knot is stronger if it has more strand crossings, as well as more “twist fluctuations” — changes in the direction of rotation from one strand segment to another. If a fiber segment is rotated to the left and to the right as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot.

Wisely, the authors point out that there is no winning knot in this. It all depends what the knot is used for: suturing, sailing, climbing, construction and all other areas depending on knots to keep volumes bound to each other.

Visually I borrowed the background from the Knot Atlas, arc presentation  of a 8.0 knot. The planar picture of the knot in which all arcs are either horizontal or vertical creates very dynamic lines  explored based on a Mango-based color theme.

I figured that sailing toward Macapa, the city of Mangos, after 7 weeks and 2,800 miles from Null on the ocean, any sailor would be looking forward to taste that succulent fresh fruit plentiful on Macapa’s food stands.

02-23

Inverted Möbius

Week 3, 1,200-some (nautical) knots from Null island.

Reflection of an inverted Moebius strip on my compass box. Virtual knot such as this one are made possible using parameters of longitude and latitude on a 3D sphere. The Möbius transformation minimize area distortion and is used to converts 3D brain scans in 2D readable maps.

In addition,  in stereovision,  the 3-rung Möbius ladder helps chemists synthesize molecules. Quite an impressive resume for a surface discovered by German mathematician Möbius in the mid 1800s.

More on the Möbius strip and the Knot geometry project on Patreon @@http://bit.ly/knotgeometry

01-26

2018 update

The Geometry of Nature project is starting to move around.

An article I wrote after the work I did on 02-03  has been just been published by IGI-Global under the title The Four-Color Theorem and the Geometry of Nature

Fig06-fluorite-PR