Fractal knots      

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I developed a method of manufacturing fractal knots.

The method works well for any odd, having more than 3 numbers leads.

Fractal dimension (Hausdorff dimension): 1

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> Fractal knots two-sidded

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Knots for the odd number of leads     

(probably for single strand, number of times and number leads must be coprime)

1 x

2 x

3 x

3L

3L

3L

1 x

2 x

3 x

5L

5L

5L

1 x

2 x

3 x

7L

7L

7L

1 x

2 x

3 x

9L

9L

9L

1 x

2 x

3 x

11L

11L

11L

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Example 7L(3x):

            Friendly Ghost :)

Used diagrams

            Used tool

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    Even leads (reduction method)

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Mixed types

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Dome knots (mix: fractal knot + THK)

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More examples:

                  See: ABOK #2222





Tree knot (mix: fractal knot + 2 x THK)




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Fractal knot two-sided (Hourglass)



Example 14L(3x)two-sided:



I decided to transform the open knot into the torus. You can see here the steps of this transformation.

At the end I cut and sewed the edges according to the rule:

Connection bight - bight.




Fractal knot toroidal


In order not to cut and sew the edges I developed a pattern to plait that knot.

Unfortunately you can not remove a knot without destroying the pattern.




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