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Combining Fibonacci spirals


Adaptive Hypercycle of Sustainable Psychosocial Self-organization (Part #9)


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In relation to a spiral presentation of hexagrams in Fig. 2 (above), several possibilities may be explored of combining Fibonacci curves to constitute "solar rays", as suggested by the following.

Fig. 5: Patterns for consideration in designing a configuration of hexagrams
Rotated combination of eight Fibonacci curves to provide a pattern
for positioning of hexagrams (one spiral arm for each "house")
Fig. 5a: "Clockwise" rotation Fig. 5b: "Counter-clockwise" rotation
Spiral pattern in designing a configuration of hexagrams Spiral pattern in designing a configuration of hexagrams
Fig. 5c: Superimposition of "clockwise" and "counter-clockwise" rotation)
(hexagrams in Fig 2 could be appropriately
positioned at intersection points of the two rotations)
Fig. 5d: Typical graphic rendering of Fibonacci pattern,
notably found in the sunflower seed arrangement (see Fig. 7a and 7d)
Superimposition of clockwise and counter-clockwise spirals Superimposition of clockwise and counter-clockwise spirals in a Fibonacci pattern

Of interest with regard to the co-occurrence of several hypercycles is the work of Kazumasa Oida (The Birth and Death Processes of Hypercycle Spirals, 2002)


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