10-direction clock

[Rainer Rosenthal]

Robert Israel wrote:
> I'd prefer to put the clock in the complex plane with
> "0" at 1 and "1" to "9" counterclockwise. 
> Then ... Thus one set of ways to list each achievable spot once
> would correspond to enumerations of Z^4, where 
> (z_1, z_2, z_3, z_4) in Z^4 corresponds to a number m
> such that r_0(m)-r_5(m) = z_1, r_1(m)-r_6(m) = z_2,
> r_2(m)-r_7(m) = z_3, r_3(m)-r_8(m) = z_4, r_4(m) = r_9(m) = 0.

That sounds very interesting and I know of approaches in the
Al Zimmermann contest "Snakes on a Plane", to refrain from
ugly floating value computations and to use integer coefficients
together with the appropriate root of unity.

I just couldn't resist depicting the first 600 decimal digits
of Pi in a snake-like manner. With "0" you go backwards, with "1"
you turn sharp right, with "2" and "3" you turn more or less to
the right, with "4" you turn only slightly right and with "5" you
move straight on. The digits "6" to "9" bring you to the left.

Using the first 600 decimal digits of Pi in this way traces through
the plane as follows:

http://www.rwro.de/Demonstrationen/Pi600.jpg

The "snake" starts at the red end, becomes blue then and is green
in the end. 

Cheers,
Rainer