The reason for the 35-times or 7-times random write is this:
Oversimplified - Disks are divided into circular TRACKS, which are then divided into SECTORS. Disk head read-write is essentially like a cassette tape recorder. When you write, you run current through a magnet (the head) change the orientation of magnetic particles suspended in a gel (emulsion). To read, the head reads the magnetization as it passes over it and a current is induced in the head.
Writing once, you may not completely re-orient all the magnetic bits. Supposedly, there may be residual magnetization from previous bits. Hence, re-write the same place over and over again with random values (sort of like “scribble all over”) so the original setting can’t be distinguished.
Also, the head wanders. The head has very precise control to stay in the circular track, but with vibrations, thermal changes, etc. the control is not extremely precise. As I understand it tech now or at one time used the feedback from the wandering head - as the read signal faded, it indicated “you’re wandering off track” and like tuning the old analog radio, dialed the head back to the center of the track. As a result, there may be some residual magnetization left in spots because not every re-write covers the exact same track real estate as the previous write.
Of course, that sort of data recovery is NSA territory. You gotta really really want to get the data to spend the time analyzing, finding fragments of files, and trying to reconstruct files from the pieces (sort of like the Deas Sea Scrolls - type jigsaw puzzles.)
The simplest data recovery is this - when you delete a file, you don’t. A file is a directory entry that points to a chain of sectors that make up the file. “DELETE” flags the directory entry as deleted (special code in first byte of name) and appends the file sector chain to the free space sector chain. As a result, depending on amount of free space and how much you write to the disk, your complete file (the whole sector chain) may be intact and findable. that’s what “un-erase” programs do.
It’s a bit more complex, too. When you write a file, it uses a series of sectors obtained from the free space chain. If there’s not exactly, let’s say, even 4K’s of data, then if sectors are 4K the final sector of th file will write the end of the file, followed by a code bytes saying “this is the end”. If there was data in the sector from before, it may still be there unchanged - so fragments of your old file hang around as the tail end of new files.
Similarly, with MS Office and many other programs, when you “SAVE” it may not re-write the file; It writes the new file as a temporary file, deletes the old file, renames the new; so yor free space may contain 10 copies of your document even though all you did was edit it 10 times. Plus, windows likes to put stuff in the recycle bin for easy recovery. Empty recyle bin just sticks it in the free space queue.
Some programs like to keep logs - sort of like phone call records. The data might not be there, but file names, times, etc. might be. Plus, if an error (or even some informational records) may show up in event viewer.
Internet explorer likes to keep megabytes of old data, including cookies pushed to you by websites that indicate details like the time and date you visited. This sort of operating system data is hidden from normal prying, you have to enable “show hidden files” and “show system files” to see these.
Also, some program data (last files opened, etc.) may be hiding in your registry entries for that program.
So there are plenty of ways to dig through a computer and see what someone was doing, whether they googled “Cholorform” for example… That does not even begin to cover what places like google have kept on their website logs, tied to your IP address, OS and browser versions, and other computer-identifying data.