| Trefoils with a fixed radius | Trefoils drawn with a tube of radius R(P) |
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| 6 sides rope length 214.19 |
Since the trefoil has stick number equal to 6, the thickest equilateral conformation is cramped. If one allows the edge lengths to change during the evolution, the minimum rope length conformation has ropelength around 63. |
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| 9 sides rope length 44.35 |
Conformations of the trefoil with side numbers divisible by 3 tend to outperform the trefoils with similar edge numbers that are not divisible by 3. Here we see a trefoil with very few sticks which has found a symmetric conformation. |
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| 13 sides rope length 40.03 |
Since 13 is not divisible by 3, symmetry is out of the question. This trefoil does not have enough sides to overcome the awkwardness of the unnatural number of edges. |
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| 27 sides rope length 34.15 |
Again 27 is divisible by 3 so we get a very symmetric picture. One can start to see the three almost circular loops. Furthermore, notice the way that the knot passes through the centers of these circles perpendicularly. |
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| 41 sides rope length 33.44 |
There are enough edges now that the knot can overcome the unnatural number and evolve to a symmetric-looking conformation. |
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| 100 sides rope length 32.87 |
The knot almost looks smooth here. The knot has aligned itself to take fill in every possible bit of volume. |