Quantum knot

I’m not a sailor.

The only knots I know are mathematical knots, but I suspected it. For a few weeks now, my scripts were starting to behave strangely when calculating my longitude and distance.

I must be near longitude 180º when West turns into East and Yesterday becomes Tomorrow.

Confusing? Not for a Quantum knot. It all starts with an unknot like this one. Untangle the loops, it turns into a perfect circle! 

Quantum theory is not an abstraction, it’s very helpful in optics, chemistry, and for the understanding of gravity. 

All in this proudly standing unknot-knot!



Dolphin dance

A cloud knot or a school of Dolphin dancing around me in the middle of the ocean? At longitude 165º. W. on the equator line, there is plenty of time to dream new dreams.

Cloud knot – it starts with a double coin knot. The knot is created through a weaving technique.  Double coin knot? It is a decorative knot that appears in many ancient Chinese art forms.  The 8.18 knot is the mathematical version of the actual double coin knot. 

Much inspiration in the clouds!

More on the Knot-geometry journey @http://bit.ly/knotgeometry


Surfing on the equator line

From the wind map wave pattern to the surf-knot, my connection this week is the Surfer program in which I created an iteration of the Klein knot!  Mysterious and silent like a sea shell, yet a beautiful geometry to surf into.

Actually, to create a Klein bottle you need to apply 4-Dimensional geometry principles. A space many surfers are already very familiar with, I am sure.

More on the equator wind-map, the Klein knot and the Knot-geometry project @http://bit.ly/knotgeometry



Silent embraces

Another iteration of the figure 8 knot in honor of the people of Tuvalu.

The people of Tuvalu, a small cluster of atolls in the middle of the Pacific are preparing to leave and will be gone soon, as the water level is raising every day. Tuvalu apparently means 8 standing together. My double figure knot goes to them on week 26 of the Knot journey.

The 8.8 knot has such smooth, flowing lines, it brings Brancusi to mind. He must have studied it too!

And yes, the image background is a satellite picture of the atolls that soon will be little dots at the bottom of the ocean in the middle of nowhere.

More on the Knot geometry project, wind-map and the 8.8 knot on Patreon




Coral knot

Coral reef, reef knot, square knot. Free word association? Maybe, maybe not, as little specks of land are coming at me above and under me, on week 24 of the Knot geometry journey.

Fractal patterns have been observed in the small-scale structure of shallow-water coral colonies. The coral stitch, also called the coral knot stitch or coral knot, is a line stitch made of knots. It provides an impromptu canvas for this square knot shape gliding over it. The 6 -fold symmetry of the knot echoes the 6 fold symmetry of the coral on this iterated square board from  Jaime Rangel-Mondragon



Black pearl

Where do black pearls come from?

Some may say from oysters in some far away Pacific island. But how about a 16 cells, 1040 fragments polytope hexadecachoron?

In 4D geometry knots can be unknotted. Conversely, unknots can start their journey as 3D knots squeezing in between the vertices of this very abstract 16-cell polytope.

Starting with 2D planar geometry we can build a 3D ribbon and project it in 4D.  That’s what I did in KnotPlot to look into the interaction between a knot and a 16 cell polytope.

It may not solve the black pearl mystery, but it creates an elegant string for this unusual occurrence that happens only in one out of 10,000 pearls.



A slice knot

A 10.3 knot.  This illustration takes a little explaining:

– The foreground object is a 10.3 slice knot with a Voronoi texture

– The central design was inspired by the 1922 W.C. Handy’s book “Tattooing in the Marquesas”

– On the upper left a WindMap of Planet Earth this week. The disks around the planet indicate that this illustration is about sliceable knots, meaning knots that can fit around a disk. The small sphere in the center of the planet is the positioning of the Knot-Geometry project this week, middle of the Pacific, on the equator line, and north of the Marquesas islands.

More on Voronoi, the slice knots & the Knot-geometry journey @http://bit.ly/knotgeometry



Night Sky over the Marquesas

Longitude 131 W on the equator line. That’s what you could have seen last night sailing near the Marquesas island, thanks to Google Earth.

For good measure, I added a one-twist knot. Elegant and somehow spirally looking, it blends well into this galactic skyline.

More on the one-twist knot and the knot geometry project on Patreon


Quipu knot

Quipu” is a Quechua word meaning “knot”. According to  the Quechuan culture, the number 731 is represented by 7 and 3 simple knots and a figure 8 knot. In mathematics, the closest knot relating to this number would be the 7.3 knot.

Visually, it could stand as a proud and a well-balanced accounting statement!

To add to the mood, as the knot-geometry project is within sight of the Marquesas islands, I have borrowed a design from the local complex tattoo  tradition as a background for this week’s illustration. More about the 7.3 knot  and the Knot geometry project @http://bit.ly/knotgeometry



Laocoön’s sea serpent knot

In the middle of the Pacific ocean, an Ashley knot on the horizon. Maybe, Laocoön’s sea serpent on his way to Troy followed by two bundles of squids? Greeks love calamari!

Actually, this knot was developed by American knot expert Clifford Ashley in 1910. It was inspired by a stopper, a kind of a figure 8 knot, he saw on an oyster fishing boat. Add a sprinkle of Gauss code on the knot and that’s what it transforms into.

The Gauss code represents a knot with a sequence of integers. However, rather than every crossing being represented by two different numbers, crossings are labeled with only one number. When the crossing is an overcrossing, a positive number is listed. At an undercrossing, a negative number.

The ocean is an endless source of inspiration!

More on Ashley knot and the Knot-geometry project on Patreon