{Chaotic Determinism (+ Extracts) [continued (6)]}[3rd August 1988]

[Redbook5:250][19880803:1949b]{Chaotic Determinism (+ Extracts) [continued (6)]}[3rd August 1988]

.1949

[continued]

*‘The Complex Boundaries of Newton’s Method. The attracting pull of four points – in the four dark holes** – creates ‘basins of attraction’,*** each of a different colour, with a complicated fractal boundary.**** The image represents the way Newton’s method for solving equations leads from different starting points to one of four possible solutions (in this case [–] the equation is x⁴ – 1 = 0).’#

#*

*Points of particular relevance to C[ircles] A[nalysis]. <880807>

{(&↓[[Redbook5:252][19880803:1117]{Chaotic Determinism (+ Extracts) [continued (10)]}[3rd August 1988],])}

**(at the cardinal points)

***(around each of them)

****(between them, along the diagonals, showing colours from the other 2 quarters as well, and predominantly). {See [Redbook5:252][19880803:1117]{Chaotic Determinism (+ Extracts) [continued (10)]}[3rd August 1988],] p252}

#(cf Pascal n=4) ([[Redbook5:222-223][19880724:1443g]{The Sphere [continued (7)]}[24th July 1988]] p223)

[But note that the number of attracting points varies, (presumably) depending on the power of x; eg x³= 1 shows 3 attracting points. <20181103>]

#*Ibid [Gleick, ‘Chaos, Making a New Science’, Heinemann, London, 1988], pp172-3, Photos Inserts Caption) (& see the colour photo)

[continues]

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