I am looking for a representational (but preferably spatially
accurate) view of how a small number of neurons (say 100) are
connected to other neurons, in a similar way that molecules can be
represented as 3D ?stick and ball? models.

Motivation/context for this question: I can imagine how 1 neuron could
be connected to 6 other neurons (for example as a cubic lattice), but
I find it hard to visualise how 1 neuron can be connected to 1000
neurons (apparently the number of connections per neuron in an
animal?s brain).  Any insight into this would also be appreciated.

Hi Xman, 

Good question! When you think of all those nice neat molecular models
we were shown in Biology class, it does seem that the structure of
interconnected neurons should be something we can represent with a
similar model ? in which case, you?re right; thousands of
interconnections doesn?t seem feasible.

But, let?s take a look at what a neuron is made of and how it works.  

===========================
NEURONS AND HOW THEY WORK
===========================

Think of a neuron as a multi-armed creature like a starfish. Here?s a
2-dimensional photo:

The European DANA Alliance for the Brain: neuron.jpg
http://www2.unil.ch/edab/images/presse/neuron.jpg

The neuron is made up of 3 parts: 

1 - The body or soma; 
2 - Hundreds of ?arms? called dendrites for receiving signals; 
3 ? One long arm called an axon for sending signals. One axon may
branch into thousands of terminals.

Axons and dendrites pass signals to each other via connections called synapses. 

Here is a simple diagram:

The Mind Project: neuron_synapses.jpg
http://www.mind.ilstu.edu/images/tour_curriculum/neuron_synapses.JPG

A good explanation as to how neurons work is here: 

?The dendrites can be likened to a bushy antenna system that receives
signals from other neurons. When a dendrite is stimulated in a certain
way, the neuron to which it is attached suddenly changes its
electrical polarity and may fire, sending a signal out along its
single axon where it may be picked up by the dendrites of other
neurons.  Considering the small size of the neuron's body, the length
of an axon can be considerable, up to several meters in the neck of
the giraffe. Thus the firing of one neuron can influence the firing of
another one a considerable distance away.

For one neuron to influence another, the two must be connected, and
this is accomplished by junctions called synapses (figure 5.2). These
synaptic junctions usually connect the axon of one neuron with the
dendrites of another, a typical neuron in the cortex of the human
brain having about 10,000 synapses.?

Without Miracles - 5 Brain Evolution and Development:
The Selection of Neurons and Synapses
http://faculty.ed.uiuc.edu/g-cziko/wm/05.html

Up close, here?s a single dendrite connecting to multiple axons via synapses:

Spinal Cord Injury Treatment Research: Synapse.gif
http://www.sci-recovery.org/images/synapse.gif
 
Now, those are simplified 2-dimensional drawings. Let?s take a look at
what a real neuron looks like.  Here is a computer model constructed
from an actual 3-d microscopic photo of a single cortical neuron. The
cell body (soma) is represented in blue. The neuron?s dendrites
(receive electronic inputs from other cells) appear in green, and the
axons (cell?s output branches) are represented in red.  The white dots
represent the locations of boutons. Boutons are where synapses occur.

3-D Camera Lucida: neuron_1985.jpg
http://www.dpo.uab.edu/~jgemmill/Visualizing_Neurons/3D_Camera_Lucida/neuron1985.jpg


Now imagine all of those synapses connecting to similar neurons ? and
each of those connecting to hundreds or thousands more. You can see,
there would be no structural regularity to it. It would be a ?huge?
(in microscopic terms) tangle of interconnected neurons, dendrites,
and axons.

=================
IMAGES
=================

Here are some images of multiple interconnected neurons:

Neural Engineering ? 01-neurons.jpg
http://www.njit.edu/publicinfo/images/01-neurons.jpg

Nerves: images6.jpe
http://www2.unil.ch/edab/images/Cerveau/cellule_nerveuse/Photos/Image6.jpe

Structural Plasticity of synapses in vivo: two-photon microscope image.
http://saturn.med.nyu.edu/research/mn/ganlab/images/figure2.gif

A very nice artist?s rendition (and explanation) on this page (Click to enlarge): 

Pittsburgh Tissue Engineering Initiative: Neurons
http://ptei-brains.cfa.cmu.edu/under/brain/neurons/intro01.php

====================
NEURONS: THE MOVIE! 
====================

I?ve saved the best for last. Go here and download the short
fly-through mpeg movie. It?s only 7mb and well worth watching. This
should give you a clear visualization of how hundreds or even
thousands of neurons can interconnect:

Flythrough of V1 (Primary Visual Cortex)
http://www.psc.edu/biomed/brainmovie/

Also see other images on that page. 

==================
MORE INFORMATION
==================

Neuroscience for kids: Types of neurons
http://faculty.washington.edu/chudler/cells.html

Wikipedia: Neuron
http://en.wikipedia.org/wiki/Neuron

How Stuff Works: Neurons
http://health.howstuffworks.com/brain1.htm


Your question was interesting and I?m so glad to have found the movie!
What a great way to illustrate how our neurons work together.

Let me know if anything is confusing and I?ll be happy to clarify. 

Thanks for a great question!

-K~

Search terms used:

In Google Image Search --- 

Synapses
Neurons
Axons
Dendrites

In Google ?---
Neurons
How stuff works neurons

Overall a good search performed, but not exactly what I was looking
for (ie a more geometric abstraction of neuron structure). cheers

Go have a look here

http://www.crd.ge.com/~avila/haptics/neuron_ex.html

Best bet you can do is an image search on google with the keyword neuron

Ah, I think the penny has dropped, the synapses bifurcate, so each
synapse sends/recieves signal to/from several neurons.  So neurons are
not connecting to other neurons 'uniquely'.

It's still a little difficult to figure out the 'geometry' of the
neuronal structure because of the 'squiggly' nature of synapses.  Did
you find any 'stick and ball' type models?

I still have many questions (which I'll probably find by more careful
reading of the provided links). For example how *far* do neurons
connect to each other?  Obviously adjacent neurons are (or at leat can
be) easily connected, but can a neuron connect to another neuron that
is, for example, 4 neurons away (admittedly a difficult question
because of the irregular nature of neuron structure)?