@acer 

This response is truly comprehensive - and covers all my requirements ... and then some!

Many thanks for this - I'm obliged.

@Carl Love 

Thanks for this, Carl - I like this approach.

Re-thinking this, I seek a contour plot;  curves that represents the relationship between x and z for different k-values. I do like your 3d solution, so I will certainly make good use of this.

@acer 

Despite being content with the assistance so far,  did try dialling values to reduce the jagged edges - with no luck.

Thanks for this.

This makes a great difference to the visuals.

@Kitonum 

That's also very convenient.

Thank you!

@vv 

That does the trick! Very nice method.

Thanks a lot.

@Kitonum 

I'm much obliged for your quick response and the advice ... this is very useful to me, so thank you  very much.

Notice the contourplot for z at the end.

Do you know if it is possible to obtain a 2D contourplot like this to show the y-contours in the x-z plane?

Thanks again!

@Carl Love 

Yes .... that's a good idea. 

I find this procedure works well and is very useful.

Again - my thanks to you.

@Carl Love 

This is very useful ... and very efficient, so thanks again for your creativity.

@Carl Love 

I appreciate the quick response.

Using the procedure, AssignToClusters(U), I can see how many points are associated to each cluster but I still cannot obtain their coordinates. Can you tell me what I am doing wrong? 

Thank you.

@mehdi jafari 

Thank you ... that's a nice formulation.

I appreciate the help.

@Kitonum 

Yes - that did the trick!

Thanks for your help. I appreciate it.

@Kitonum 

Thank you for the timely help. I appreciate it.

Do you know of any way to change one of the functions to display as an animated column chart?

@acer 

Yes - the example is indeed trivial (deliberately).

Sorry for the confusion - you have certainly addressed my query, so many thanks for these methods.

@Christopher2222

This is a great addition to my arsenal! Thanks for sharing.

@tomleslie 

Thanks so much ... that did the trick!