Your job is to create the longest period iterating quine, where the length of each program in the sequence is bounded by 500 bytes.
That is, if you repeat the following steps:
- Start with your initial program
- Run the current program
- Go back to step 2
You will eventually get back to your original program. The number of programs in the cycle is your score, which you are trying to maximize.
None of the programs may raise any errors. Each program must be run the same way as well (e.g. no different versions, implementations, compiler options, platforms, etc...) (EDIT: Yes, any external state such as that of a pseudo random number generator was included in the last statement. The external state must be "reset" after each run. If you use true random numbers, worst case is assumed.)
What separates this challenge from The longest period iterating quine (other than 100 v.s. 500) is that every program in the cycle must also be 500 bytes or less. This means that the longest possible cycle is (256^501 - 1)/255 or less. That of course is a big number, but not that big in terms of how much code it takes to calculate. So the challenge is about using as many of the (256^501 - 1)/255 possibilities as you can, not a busy beaver challenge.
The programs are not permitted to access its own source code. However an empty program is permitted if you want (as long as you follow the other rules).
Since checking the programs manually would be hard, you may figure out the score using theoretical methods. You must include an explanation of the score and correctness with your program. If you can not figure out the score, you may instead use a lower bound of the number of programs in the cycle as a defacto score. You are allowed to update this as you find better lower bounds, or if you find the exact actual score.
This is code-challenge, so highest score wins!
EDIT: It is recommended that you write what your score is in scientific notation, so that answers are more easily comparable. It is perfectly fine to have other forms of the score as well, especially if they more clearly are connected to your program. Also, readers are encouraged to edit previous answers to comply with this.