Questions tagged [knots]
Questions about exploring knot theory using Mathematica.
25 questions
1
vote
1
answer
148
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Graphic3D with Specularity and Glow
I am new to Mathematica, and I am currently using it to plot 3D figures.
My problem is when I use Graphic3D with Specularity and ...
- 13
2
votes
1
answer
116
views
KnotTheory` Passing PD Encoding of a Knot Diagram to Kh
I have a bunch of knot diagrams I would like to use the Kh function in KnotTheory to compute the Khovanov homology for. Almost ...
- 133
4
votes
2
answers
153
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Unable to use KnotTheory
I've installed the KnotTheory package, following the instructions here. But when I try to use it I get this error:
...
- 41
2
votes
1
answer
356
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Plot a Satellite Knot
I need some help to plot a Satellite or cable knot. For example, see figure A torus knot and a cable knot. (a) The red curve lying on the yellow torus is a (2,3) torus knot. (b) The embedded yellow ...
- 121
8
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4
answers
555
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RegionPlot3D KnotData
Is it possible to find or construct a RegionPlot out of KnotData? My motivation is to Texture...
- 8,920
4
votes
2
answers
478
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Issue Installing Knot Theory
I have been trying to install the Knot Theory package from the knot atlas, but have been unsuccessful. Firstly I tried the command
<< KnotTheory`
but ...
- 45
0
votes
0
answers
112
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generating torus and n-torus knots in mathematica
I am wondering if it's possible to either algorithmically generate or access a built in database of n-torus knots in Mathematica? If not, are there any known databases or algorithms which I could ...
- 1
2
votes
1
answer
441
views
How can I reduce the error estimate of numerical integration in Mathematica?
Before introducing the integral I want to go through some definitions.
Define triangles $T_1$ and $T_2$ by the points $\{a,b,c\}$ and $\{d,e,f\}$ respectively.
Define $$D(u,v,x,y) = sign(\det (y-u,y-v,...
1
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0
answers
111
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Export Basis spline information to matlab
i am new to Mathematica. I have generated the contours of this image with the following code
...
- 11
5
votes
1
answer
250
views
Orient a Knot Diagram
I need some help to orient a diagram knot
For example if I have the diagram KnotData["Trefoil,"KnotDiagram"]
How can I orient the diagram?
I have tried to find a ...
- 51
3
votes
0
answers
208
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Plotting symmetric closed loop on surface of sphere (plotting spherical knot)
Here are some my attempts.
...
- 25.1k
3
votes
0
answers
301
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Alexander polynomials for Pretzel knots
All knots, such as this torus knot,
KnotData[{"TorusKnot", {3, 5}}]
have an associated Alexander polynomial:
...
- 42.3k
3
votes
2
answers
161
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:
...
- 37
10
votes
3
answers
568
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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.
...
- 193
3
votes
2
answers
449
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
2
answers
262
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
...
- 42.3k
1
vote
1
answer
125
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
...
- 133
1
vote
0
answers
272
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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:
...
- 42.3k
2
votes
1
answer
295
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Color Trefoil-Knot
i need some help to plot a three colored Trefoil knot.
I found on Wolfram the code
...
- 133
10
votes
1
answer
359
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 ...
- 42.3k
1
vote
1
answer
174
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 ...
- 713
2
votes
1
answer
394
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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}}]
...
- 42.3k
1
vote
1
answer
189
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The point movement on the torus knot
I would like to ask about the point movement on the torus knot.
...
- 11
2
votes
2
answers
471
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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 ...
- 16k
12
votes
2
answers
454
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 ...
- 8,920