Review and analysis of scientific research and theory bearing on knowledge of Earth’s protogeobiosphere, origins and evolution of protobiont complexity, and emergence of life in the cosmos.

Pick a number, n.

Form the set S = {1, ..., n}

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Loop (i starts at 0):

 

Form a new set, Fi , by removing from S the smallest two numbers, a and b, and the sequence a+b, b+(a+b), (a+b)+(b+(a+b)), etc.

 

If S still has at least two elements, generate the set F(i+1) from remaining elements of S.

 

Repeat to generate the set of sequences, F0, ..., Fk , that covers S

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F0: 1,2,3,5,8,13,...
F1: 4,6,10,16,26,...
F2: 7,9,16,25,...

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Fk: ...

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Transform each Fi to a sequence of pairs: eg 1,2,3 maps to (1,2),(2,3)

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Divide a unit circle evenly by placing n vertices on the circle (Ith roots of unity).

 

Number the points 1,...,n sequentially by moving around the circle once.

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Map the pairs to line segments between points on unit circle.

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communicated 6 January 2018,                                                  Samuel L. Jessup

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