I remember the Spectrum Basic Programming (the book included when buying ZX Spectrum, famous UK home computer) by Steven Vickers, 1982, 38 years ago:
The quote from the Charpter 16: Colours
"Run this program:
10 POKE 22527+RND*704,RND*l27
20 GO TO 10
Never mind how this works; it is changing the colours of squares
on the television screen and the RNDs should ensure that this
happens randomly. The diagonal stripes that you eventually see are
a manifestation of the hidden pattern in RND - the pattern
that makes it pseudorandom instead of truly random." (1) (2)
In another part of the manual it also explains the mathematical properties of the built-in random generator:
"(For mathematicians only.)
Let p be a (large) prime, and let a be a primitive
root modulo p.
Then if bi is the residue of a’ modulo p (1 <= bi <= p-1), the sequence
(bi-1)/(p-1)
is a cyclical sequence of p-1 distinct numbers
in the range 0 to 1 (excluding 1). By choosing
a suitably, these can be made to look fairly random.
65537 is a Fermat prime, 2^16+1. Because the multiplicative
group of non-zero residues
modulo
65537
has a power
of 2 as its order,
a residue
is a primitive
root if
and only if it is not a quadratic
residue.
Use Gauss’
law of quadratic
reciprocity
to
show
that 75 is a primitive
root modulo
65537." (3)
---
1) It works by directly changing the "attributes" part of the memory which is directly mapped to the color of the 8x8 pixel part of the screen used for different characters (22 rows of 32 characters == 704), randomly selecting both the position on the screen and the value of the attribute, two calls per one loop pass. It's beautiful in how short the program is.
2) The appearance of "the diagonal stripes": https://ibb.co/kB2qS2L
3) Is the suggested proof online now somewhere?