A recent research paper shows a way to create multicolor 3D prints using a single extruder if you are too lazy to babysit the machine and switch filament. The concept: print your own “programmable” filament that has the right colors in the right place. This is the same idea as manually splicing filament but presumably is more efficient since the process works with one color at a time and doesn’t repeat. In other words, to print the 64 squares of a chessboard you’d swap filament at least 64 times on each layer. Using programmable filament, you’d load one spool, print half of the filament, load another spool, print the other half, and then finally load the newly created filament and print the chessboard. Notice that the first two operations aren’t printing the chessboard. They are printing the spool of filament you feed through on the third pass.
There are machines made to do this, of course, although they generally just splice lengths of filament together for you automatically. Using one filament solves the problems of keeping multiple heads in alignment as well as the added cost and complexity. However, you now have different problems such as the transition between materials and knowing exactly how much material will be at each point in the print.
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