Wiring 8x8 LED matrix

My current project involves writing patterns to an 8x8 LED matrix using two 74HC595 shift registers. I am using a 1088AS matrix for which I found the attached pin allocation diagram. I do not understand the apparently random position of the pin numbers in the diagram.

The pin outputs from the shift registers are, as usual, 15, 1…7. Do I connect the shift register outputs to the corresponding pin numbers in the matrix, or do I connect them to the column and row numbers?

The '595 pin numbers have nothing to do with the matrix pin numbers. You need to connect them in a logical manner.

Your matrix has 0-7 columns, and 0-7 rows. It's up to you to understand where the 0,0 location is - lower left, lower right, upper left, upper right? Then wire up Q0 from one shift register and Q0 from the other to the R0 and C0 pins and work up to the Q7s and R7/C7

Similarly if you used a MAX7219, you'd have to know where to connect Segment A (or maybe decimal point)/Digit A up to to turn on the 0,0 LED. It's pretty easy to get them incorrect, I use wirewrap sockets & 30 AWG wirewrap wire so I can change them easily when prototyping (unless I've worked it out on a solderless breadboard before hand).

Read this

This post describes how to interfaced a 8x8 LED matrix