LTSpice model of a NAND gate implemented with 555 and diodes. From there it was a simple matter of adding a few diode-resistor networks to the input, to effect a NAND2 gate and a NOR2 gate.

The NAND gate is a circuit that outputs '0' when both inputs are '1', and '0' otherwise, so if you arrange the NAND gate as follows, the Invert circuit is completed.