Thanks to all of you who responded to this questions.  You've definitely
given me some good ideas to try.  The four responses I've received so
far are listed below.

Gary.

***************
Yannick Leduc offered this idea for circles sized on the number of
points at the given location:

Hi Gary,

        this solution will work if your overlapping points are exactly
at
the same coordinates.

First, you need to add as columns the X and Y coordinates to your point
table using CentroidX() and CentroidY()
Then, perform a query on your table where you will group your data
around X
and Y coordinates. It should looks something like this:
Select Columns: Xcoord, Ycoord, count(*)
>From tables: your_point_table
Where conditions:
Group By: Xcoord, Ycoord
Order By:
into Table Named: Grouped_points

Then, save the query's result into a new table (Save Copy As) and open
it
Then, create points from X and Y coordinates (Table>Create Points...)
Then, create a graduated thematic on the count column.

Finally, you should be able to see a circle where the radius is define
by
the number of occurence at the same location.

I'm not fully operational with english. I hope you have what you need!

Salutations!

Yannick

***************
Jason Adam had this idea for creating an individual values theme based
upon the categories that occured at the same location (I especially like
this idea because it makes labelling at lot easier as well):

Gary-
I think ideally you would have one row for each location, and multiple
columns that would be filled with the data that exists at that point.
Then
to make the thematic map you'd have one final column where you
concatenate
all the data together ie category1+category2+category3+....  Then when
you
make an Individual thematic you could assign the points "category1" as
one
symbol, "category2" as one symbol, "category1category2" as another,
"category1category2category3" as yet another, and so on.  Just edit the
Legend text to reflect what the codes mean.
Good luck,
Jason
せカせЙせカせЙせカせ
Jason Adam
Computer Draftsperson
Monopros Limited
Toronto, ON
[EMAIL PROTECTED]

***************
Julie Kanzler offered several possible solutions (I like the starburst
idea):

Gary:

I have been in your situation many times because I map a lot of
sampling data and monitoring sites. Shifting a sample site is
equivalent to falsifying the data! In the past I have generally done
one of a few things:

1) used star-like symbols, where the number of prongs refers to
the number of samples the symbol represents.
2) used a thematic point map where symbol size represents
the number of samples.
3) used a single symbol, but rotated the symbol in place. This
is most useful when the rotations can refer to some element
of the data. I assigned rotations to points based on the data
collection date.  The result is that samples collected during
different sampling events overlay without obscuring any. This
is easier to do in ArcView.
4) used a combination of filled and non-filled symbols.

I hope these give you some ideas.  If you get a chance, let me
know what you end up doing ... maybe I can learn something!

Julie Kanzler
GIS Analyst/Programmer
Wyle Laboratories
Arlington, VA
(703) 415-4550 ext. 20


***************
Phil Atkinson suggested using continous theme shading which doesn't
really work for my situation since we are interested in the exact point
locations but may work for other situtations:

Gary,

We use density estimation to produce a continous density surface using
mapbasic. I'll publish the code in 1-2mnths..

Phil


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