How do I programmatically trigger the RESET vector, and bring a 6502 CPU back to the state it was when it was first turning on?

The nearest you can do is to execute:

but this only resets the CPU, not any peripherals, so it's not really the same as a power-up reset.

Dave

If you'd like to trigger a hardware reset, you can wire up a pin from your VIA to the reset pin, being careful to never set it as output high (or preferably add a diode with its cathode towards the VIA for safety). Again that's not like cycling the power but it will reset more peripherals

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BB816 Computer YouTube series

For interest, there are threads over on stardot explaining the rather different situations of the BBC Micro and Acorn's Electron, with respect to simulating a cold boot:
How to force a hard reset (CTRL+BREAK)?
Simulate a cold boot on the Electron

In effect, there are two challenges: resetting all the system state which would have been reset by powering up, and getting the OS to do the things it would do at power up.

Thanks, I was able to code up a soft reset proc to reboot the CPU with the JMP instruction.