#190: Random rope

When making a braided rope, a process akin to plaiting takes place which can be thought of as three strands at a time being linked together.

Rope and braids exhibit the emergent property that their load carrying capacity is greater than the sums of the capacities of the individual fibres. Braids tend to fail, however, when weaknesses in different fibres, which are randomly distributed along the length of each one, find themselves in alignment. To help reinforce such weaknesses, the fibres are woven regularly and tightly, but this limits flexibility.

In a 1-D cellular automaton (CA), the state of three adjacent cells specifies the state of the cell at the next level down in the pattern (See here). This is not unlike a process of braiding.

We can interpret whether a cell is black or white as meaning that the corresponding fibre in the braid is ‘over’ or ‘under’. (In this way, a conventional plait rule would look like 001-> 1, 100->1, etc…) The amazing thing about such CA systems is that they can generate something very like randomness, using only simple starting conditions and rules. Rule 30, as shown, is one such randomlike rule.

Today’s invention is therefore to use Rule 30, or similar ones, to form highly flexible braided ropes in a deterministic way.

(The sequence of fibres in the diagram starting at the top centre position and running vertically downwards would be something like …oouuouuuooouoouu… (with ‘o’ meaning over and ‘u’ meaning under) ie a continuous but almost random, and therefore highly flexible, weave).