"Xorshift RNGs" by George Marsaglia describes a very efficient system for generating high-quality random numbers using very little compute and storage.

For a simple random number generator running on an embedded CPU we're unlikely
to be very concerned with cycle lengths --
a cycle of 2^{32}-1 is perfectly acceptable.
Marsaglia suggests coefficients (13, 17, 5) for a 32-bit generator. So we have C code:

uint32_t seed = 7; // 100% random seed value static uint32_t random() { seed ^= seed << 13; seed ^= seed >> 17; seed ^= seed << 5; return seed; }

This is simple enough to give excellent performance on an 8-bit CPU.
Note that `seed` never reaches zero; in fact if seed *is* zero then `random()` returns zero every time.

This 32-bit ANS Forth implementation also has a `setseed` function which can be safely called
with any 32-bit integer.
`setseed` handles the problem value of 0 by mapping it to -1.

```
variable seed
7 seed !
: random ( -- x ) \ return a 32-bit random number x
seed @
dup 13 lshift xor
dup 17 rshift xor
dup 5 lshift xor
dup seed !
;
: setseed ( x -- ) \ seed the RNG with x
dup 0= or \ map 0 to -1
seed !
;
```

As a quick trial, plotting 65536 random pixels in a 256x256 grid on a Gameduino 2 gives no obvious patterns: