There may be chaos still around the world

George Santayana

There may be chaos still around the world,
This little world that in my thinking lies;
For mine own bosom is the paradise
Where all my life’s fair visions are unfurled.
Within my nature’s shell I slumber curled,
Unmindful of the changing outer skies,
Where now, perchance, some new-born Eros flies,
Or some old Cronos from his throne is hurled.
I heed them not; or if the subtle night
Haunt me with deities I never saw,
I soon mine eyelid’s drowsy curtain draw
To hide their myriad faces from my sight.
They threat in vain; the whirlwind cannot awe
A happy snow-flake dancing in the flaw.

convergenceto Chaos means something more specific to the mathematically inclined. This little picture shows the pattern of convergence for the complex roots of (X^3-1) with Newton’s method. The colour shows which root was found for each starting point. There’s nothing that vaguely resembles a continuous boundary between regions. (The picture’s left-handed – the Red is X = 1.)

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