Can I plot a grid in the x-y plane when subdividing the interval between each point?

Hi,

This is my posting to this forum, so I hope I am following all procedures

I am thinking about a problem to (hopefully) solve in Excel using a pair of coordinates to form a grid in the x-y plane.
This is easily constructed - but I want to reduce the intervals between each point so that the number of blocks in the grid increases and I wish to obtain the x and y coordinates for each point as the scale varies.

I hope the attached example clarifies this.

A grid is constructed in the x-y plane.
The values of x range from 1 to 4 and y ranges from 1 to 3. These ranges are fixed.
Each point is defined by the 12 pairs (1,1), (1,2), ..., (3,3), (4,3). These 12 points make up 6 blocks in the grid - see Fig 1.

Suppose now, that we wish to split the interval between each point in two (n=2) in order to produce a greater number of blocks in the range.
This will require 35 points that enclose 24 blocks in the grid. See Fig 2.
If the intervals are then split in three (i.e. n=3), this will produce 54 blocks in the grid, and so on.

I am looking for a way to obtain the coordinates of each x-y point for successive subdivisions (for any general integer, n).
There are several values of n that I wish to model and plot, so a formulaic approach would be very useful.

Can anyone suggest a way to do this in Excel?
Thanks for reading!

Hi ,

When n = 1 , the increments are 1 , as in 1 , 2 , 3 and 1 , 2 , 3 , 4.

When n = 2 , the increments are 1/2 = 0.5 , as in 1 , 1.5 , 2 , 2.5 , 3 and 1 , 1.5 , 2 , 2.5 , 3 , 3.5 , 4.

When n = 3 , the increments are 1/3 = 0.33333 , as in 1 , 1.33333 , 1.66666 , 2 , 2.33333 , 2.66666 , 3 and 1 , 1.33333 , 1.66666 , 2 , 2.33333 , 2.66666 , 3 , 3.33333 , 3.66666 , 4.

So in the general case n , the increments should be 1/n , as in 1 , 1+1/n , 1+ 2/n , 1 + 3/n and so on.

Narayan

Thanks for this ... very useful.