{Chaotic Determinism (+ Extracts) [continued (8)]}[3rd August 1988]

[Redbook5:251][19880803:1949c]{Chaotic Determinism (+ Extracts) [continued (8)]}[3rd August 1988]

.1949

[continued]

(Fiegenbaum’s ‘constant’, 4.669, seems familiar, as though I had met it before somewhere.)*

It’s an unfortunate coincidence – but unavoidable from my point of view – that two of the three [fictional] Archetypes on the ‘technical’ side [of the Circle] in [2] bear the same names – […] – as two of the three physicists whose work on a particular problem (phase transition, I think) in the Sixties led to the maths of chaos.**

*Perhaps from (e.g.) a New Scientist article? <880804> [&/or possibly in relation to the Mandelbrot Set; see [[Redbook4:271-274][19871230:0017]{The Mandelbrot Set}[30th December 1987]]]

[{]It seems to be the convergence rate at which the period-doublings come faster and faster (ie accelerate!) ie the ratio of 2^nd to 1st, & of 3^rd to 2^nd, etc.[}]

[In the context here, it is of course the approximate value of n=4 for 2ⁿ at which the Outer Circle starts significantly breaking down if each value of n from n=0 is allocated sequentially to the next cardinal or diagonal point on the circumference starting at the ‘top’, i.e.

+C†I~ Attraction =0,

xA S~ Ordination =1,

+M~ Outer Action =2,

xLU~ Complication =3,

+MkA~ Distraction =4,

xPJ~ Fragmentation =5,

+KG~ Revolution =6,

xSR~ Simplification =7,

+C†I~ Crisis =8;

see [[Redbook5:218-239][19880722:2307]{The Sphere}[22nd July 1988]],ff], & VI.]<20180911>

[& see [Redbook5:253][19880804:1354]{Chaotic Determinism (+ Extracts) [continued (11)]}[4th August 1988]]

**Ibid [Gleick, ‘Chaos, Making a New Science’, Heinemann, London, 1988], 160

[& two of the four (fictional) cardinal Archetypes in [0] onwards have the same first names as the writer’s maternal aunt and her husband. These things happen.]

& cf II. [[Redbook2:366-371[19850806:2138]{A Dream: Return through the Tunnel}[6^th August 1985]] 366-7 with the colour photo facing Ibid 172 (Lorenz Attractor, Phase-Space Diagram): it is a close (but not exact) resemblance, as I recall.

[continues]

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