BIM (BBS-ISL Matrix): How to Make

10 Easy steps to making the symmetrical BIM

After you set up your table with 10 x 10 Columns and Rows:

• (Example using the Numbers app.)

A	B	C	E	F	G	H	I	J
line	Axis # = x	PD # = x2	x2 -1	x2 -4	x2 -9	x2 -16	x2 -25	36

1. Column Headers. After -25, simply copy and paste in the PD sequence 36-49-64-… that you can copy from your own list: 1², 2², 3², 4²,... as found in Column 3 (C) below.
2. Column 2 (B) is just like Column 1 (A): type in 0,1,2,3… and drag down.
3. POWER('Axis # = x',2) is the formula for squaring the Axis #s giving the PD#=x² in Column 3 (C).
4. $'PD # = x²'−1 is the formula for ALL the remaining Columns ADJUSTED by changing the “1” with the PD cell value found in the Header immediately above. The “$” symbol means “absolute” and all subsequent calcs will use the fixed value from C.
5. Once selected, you can drag-copy the formula across the Table and then make the ADJUSTMENTS quickly.
6. Autofill the Table by selecting the TOP Row (under the HEADER) and pull down the orange-dot symbol to the bottom of the Table.
7. Because the BIM is bilaterally symmetrical about the PD, and, because the same PD #s forming the horizontal ROWS are also forming the vertical Columns, the BIM upper triangle — above the PD — will show a negative (-) sign in front of the cell values and this sign is to be ignored.
8. Below the PD, all the cell values will be (+) numbers, without any sign.
9. The PD itself — because it reflects subtracting the same PD # from itself — will be “0” and this may be color coded to reflect that and/or the ACTUAL PD values, as found on the HEADER above, can be inserted.
10. To expand or to fill in a particular Axis # — or range of #s — simply add the appropriate Columns and Rows and duplicate the above process for those values.

Color coding the Table, Columns, Rows and Cells can be done in the Numbers App Cell section. Text in the Text section, etc.

Why the 10th Column and Row? Fill that in to check your work here.

Of course for smaller BIM grids, one can simply enter the cell values by hand as all the Inner Grid (IG) values are simply the difference between their Prime Diagonal (PD) Column and Row intercepts, e.i. 16 = 25 - 9 PD values.