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Questions tagged [knots]

Questions about exploring knot theory using Mathematica.

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2
votes
0answers
71 views

Plotting symmetric closed loop on surface of sphere (plotting spherical knot)

Here are some my attempts. ...
3
votes
0answers
96 views

Alexander polynomials for Pretzel knots

All knots, such as this torus knot, KnotData[{"TorusKnot", {3, 5}}] have an associated Alexander polynomial: ...
3
votes
2answers
133 views

The design implication of PD[X[ #, #, #, #], X[#, #, #, #]]

In Package KnotTheory, there's a function called PD[] that takes a tabulated knot and returns its PD codes, for example: ...
8
votes
3answers
206 views

Issue Plotting Torus Link

I'm having an issue plotting torus links in Mathematica. What I'm trying to generate is a (2,8) torus link like the one in the picture in Wikipedia: using equations such as those outlined here. ...
2
votes
2answers
250 views

Intersection between knot and plane

I have to find, with Mathematica, the intersection between the curve defined by a knot and a plane defined by three points, in 3D space. I tried to find the intersection with ...
2
votes
2answers
133 views

Extracting tube style from KnotData

How do I extract the tube style (including lighting, viewpoint, ...) from KnotData["Trefoil"] and apply it to a space curve, such as ...
1
vote
1answer
103 views

Plot a circle in 3-D with a tangle

I'd like to plot a circle with a small tangle. I tried it but it didn't work. I want to plot it like in the picture below but only in 3-D if it is possible. What i did so far ...
1
vote
0answers
117 views

Deform a three-dimensional knot

Mathematica has curated knot data, e.g., KnotData[{3, 1}] One can extract the three-dimensional space curve in this way: ...
2
votes
1answer
134 views

Color Trefoil-Knot

i need some help to plot a three colored Trefoil knot. I found on Wolfram the code ...
9
votes
1answer
264 views

Coloring strands in braids

Is there an option, or simple work-around, for coloring each strand in a three-dimensional BraidImage differently? For instance, I'd like to render a braid image ...
1
vote
1answer
105 views

How to pre or post process KnotData “substrate”

What I'm after might be thought of as operating on the 'rope' that KnotData[] uses. Specifically, I'd like to be able to specify that the knot is to be made of a ...
2
votes
1answer
198 views

Knot diagrams and knot projection diagrams

One of Mathematica's lovely curated databases is KnotData, as you can see by running: KnotData[{"PretzelKnot", {5, 2, 3}}] ...
0
votes
1answer
129 views

The point movement on the torus knot

I would like to ask about the point movement on the torus knot. ...
2
votes
1answer
272 views

How to add color to a knot

Is there a way to use a colorscheme to a KnotData image? One way is probably convert it to a parametric form and then use ...
12
votes
2answers
364 views

Adapting KnotDiagramData to form more visually pleasing diagram

Graphics[KnotData[{5, 1}, "KnotDiagramData"]] gives but I would like to create diagrams like this remeniscent of Celtic knot designs (which I made by adapting the ...