And now for some speed tuning.

A simple way to measure the program's speed is to count how many frames 
per minute it can render. So, set it to 320x480 so it's moderately fast 
[on this ancient single-core 32-bit 1.5 GHz CPU] and count.

After fixing the stupid bug: ~24 frames/minute.

Changed array indexing from tuples to integers: ~24 frames/minute.

Merged the four arrays into one interleaved array: ~26 frames/minute.

[I'm thinking this might improve cache behaviour slightly... but 
apparently not much. Or just the cache isn't the bottleneck.]

Removed array bounds checks: ~27 frames/minute.

Removed adaptive time step: ~80 frames/minute.

[Well there's a surprise. Pitty the frames look awful...]

Added adaptive time step within RK4 as per Scott's suggestion: ~1 
frame/minute.

[Ah, but now the "error" is being calculated in a totally different way, 
so the error tolerance required to get a good image may have changed. 
What happens if I use a less strict tolerance?]

Turned down error bound: ~68 frames/minute.

[I made the maximum permissible error 10,000x larger, and the images 
still come out looking flawless. But they render vastly faster...!]

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