I do not have the skill or mathematical insight to say that absolutely. But it is a maxim to always be sceptical (naturally) and to be careful with RND. For a third time I did not get spirals with occasional RANDOMIZE(TIMER).
Thanks Qwerkey for double checking. I did my own investigation. Putting RANDOMIZE TIMER just outside of the iteration loop and running 32000 it just ran too slow. Then 1 to 10 million iteration test:
1,000,000 no spirals
2,000,000 no spirals
3,000,000 chaotic spirals that often broke up
4,000,000 chaotic spirals that did not break up as often
5 to 9 each a little better
10,000,000 pretty close to the original
This in my opinion is proof that the cyclic nature of the RND function is conducive to forming spirals. Good catch!