Thanks for the timely response.

As regards the expected values ...

Parameter a will typically take the value 0.1 and the index, m, will vary from 0.1 to 10

I'll take a look at the commands you suggested - so that will be helpful.

I appreciate your help!

@Carl Love 

Thanks so much for taking an interest in this and for providing me exactly what I need!

@jganding 

That's exactly what I was looking for!

Thanks for the quick response and the advice - especially on the use of the printf command.

I'm very grateful ..

@mmcdara 

I agree. Following your response, I reviewed the references you recommended and they are very interesting indeed.

Once again .. thanks for your help.

@mmcdara 

I thank you for taking the time to resolve this and to introduce me to the resources.

Your procedure will give me a good start! 

Thanks again!

@Christopher2222 

I appreciate this advice ... I'll give it a shot when I return to terra firma.

Thanks again!

@tomleslie 

This is exactly what I was looking for.

Many thanks to you for sharing this and for the speedy response.

Thanks for the link ... I'm sure that will do the trick!

@acer 

Hi - thanks for the quick response.

Here is the file (retrieved it from the old laptop).

Cluster_Analysis_Sep_23.mw

@Carl Love 

Thanks ... I'll do that.

@Carl Love 

I guess we'll wait and see. Thanks for persevering with this.

@Carl Love 

Hi again. 

The solution you provided is great .. thanks again.

Just a minor observation - if you don't mind me sharing. 

When I copy and paste your routines into my worksheet, the left-side labels of the dataframe equation does not appear on my screen (i.e. AtoB, BtoC, AtoC is absent). In other words, the three matrices are returned alone. However, I accidentally discovered that, when I undo the previous operation, the labels then appear!

I also noticed that when I execute your entire worksheet, it's fine!

Have you ever encountered this?

@Carl Love 

Thanks for this - this is exactly what I was looking for. 

Yes ... I modified this problem many times (hence the bug!).

As usual, your help and ideas are greatly appreciated.

@Carl Love 

I didn't notice that condition on vertical travel only - that's a nice catch!

Thanks again for a very comprehensive routine.

@Carl Love 

This is a great piece of work and is most useful to help me visualize trails - exactly what I needed.

I'm very grateful for this -  thank you!