12bit LFSR taps: [12,11,10,4]
24bit LFSR taps: [24,22,20,19,18,17]
The taps for the 24 bit LFSR system were chosen to look more interesting after the initial single bit.

For the implementation, I used 74LS series logic ICs that were laying around. 74LS86 are XOR gates, 74LS164 are serial in - parallel out shift registers, and 74LS04s are used to drive the LEDs.