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.

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.)