Reverb idea
In his reverb article, JAM mentions that the best halls had impulse responses
that looked like exponentially decaying noise.  Why not approach the problem
of constructing a "filter" with such an impulse response directly -- but not
by using the gross convolution method.  The impulse response of a filter can
be read off from the coefficients of the Taylor expansion of its transfer
function; and the techniques of generating functions could possibly be used
to construct a transfer function that has an appropriate expansion.  Note
that typical uniform random number generators are implemented using simple
recurrences -- though using modulus arithmetic; so perhaps this approach can
be made to work (perhaps with a non-linear filter?).

However, I also have another, rather intriguing idea.  So far, all the kinds
of reverberators I am familiar with have connected the individual feedback
units in either series or parallel -- but there is another alternative, more
similar conceptually to real rooms.  That is, to have all of the units share
the same feedback pack, giving a "toriodal" or donut configuration.  I.e.,
	    
	    +-----+
	    |  -m |
	+---| Z   |←--+
	↓   +-----+   ↑ g
	↓            /
 in →→→→⊗→→→→→→→→→→→⊗→→→→→→→→→→ out
	↑            \ 
	↑   +-----+   ↓
	↑   |  -n |   ↓ h
	+---| Z   |←--+
	    +-----+

This will give a greater echo density than the series connection, but will
have to be investigated to see if it does the right kind of thing.  One
obvious problem is how to ensure the stability of such a reverberator.  We
can hair this up a bit by sticking a low-pass or other filter in the common
section, and/or in the individual feedback loops.  We can even stick in an
imitation of the first chunk of impulse from a known hall.  But a method
must be found for constructing a guaranteed stable reverberator; donuts
blow up much more quickly than series.  Because they feed themselves so
much more they are both denser earlier and of greater amplitude and duration.

Any comments or suggestions?  Does the donut idea look worth investigating,
or has it been done already unbeknownst to me?

	-- Ken