f(x)=x(1-i)

[Andrew Dinn]

tamerlane writes:

> Fractal images as produced by computers are simply graphs of functions 
> containing an irrational number (where i = the square root of -1).

My understanding of the Mandelbrot set (to pick one example) is that
it is not a graph of the associated function but rather a graph of the
domain on which repeated applications of the function are assumed to
converge (I say assumed because the test for `convergence' uses a
heuristic). As far as computational complexity goes this is rather a
more industrial scale kettle of fish than a simple function such as
f(z) = z(z - i).

...

> Does the code begin with DNA? Yes, there is a 
> fear of the unspoken possibility at the end of COL 49, just as the void 
> of chaos in general generates fear - the fear of not so much the unknown 
> as the uncontrollable in our consciousness.

Fractals and chaos depend pretty fundamentally on the use of infinity
(in the shape of a dense - if not complete - number line).
Unfortunately, when it comes to humans we come in particular shaped
and sized boxes which means there are only finitely many DNA sequences
which can occur in soemthing which could still legitimately be
described as `human'. So, accounting for human variety by linking
fractals and/or chaos to genetic permutation is, I am afraid, a
non-starter. Luckily, the bound on the possible permutations is still
so mind-bogglingly large that there is more than enough variety for
any of us to be getting along with.


Andrew Dinn
-----------
And though Earthliness forget you,
To the stilled Earth say:  I flow.
To the rushing water speak:  I am.