The idea is from Petros Vrellis, a Greek artist who makes these kind of things. I consulted with him for advice and he was supercool and helpful. I used a Processing program called "weaver". The algorithm is awesome:
• Take an image file and place a circle of pins (points) around it.
• Start at pin 0.
• Scan all lines across the picture from 0 to all other pins (180 pins in mine, Petros uses 300) and assign a value for the total darkness of the pixels along that line.
• Choose the line with the greatest darkness value and draw it.
• On the image file, lighten the pixels on that line by x%.
• Repeat starting with the new endpoint.
• Continue for as many lines as necessary to get a good picture, around 3000.
That's it. Just by drawing and removing the darkest line over and over again, you get a result that looks like a photo. The program outputs a text file with a list of the points. It's then just a matter of threading 0 to 74 to 4 to 73 to 3 to 69 to 10 to 175 to 101 to...