At this link, you can find an easy-to-use ternary Laver table calculator which I have just programmed which returns specific information about the output of a ternary Laver table operation. The calculator works for very specific types of ternary Laver tables. Furthermore, at this link, you can find another ternary Laver table calculator that will return the entire (sometimes very large) output of a certain ternary Laver table operation.
The ternary Laver tables are much different than the classical and multigenic Laver tables (I used to call the multigenic Laver tables “generalized Laver tables”) computationally in the following ways:
- Unlike the classical Laver tables and multigenic Laver tables which are locally finite, the endomorphic Laver tables are infinite.
- The output of a ternary Laver table operation can grow exponentially with respect to the size of the input.
- While the fundamental operation on the multigenic Laver tables $(A^{\leq 2^{n}})^{+}$ can be completely described by the final matrix, there does not seem to be any final matrix for the ternary Laver tables. Each ternary Laver table seems to offer unlimited combinatorial complexity.
- The ternary Laver tables are much more abundant than the multigenic Laver tables. We have very general methods of constructing many ternary Laver tables.
- While the classical Laver tables and multigenic Laver tables are not suitable platforms for public key cryptosystems, it seems like the ternary Laver tables could be platforms for public key cryptosystems.
And I will probably post the version of the paper on Generalizations of Laver tables (135 pages with proofs and 86 pages without proofs) without proofs in a couple of days. Let me know if the calculator is easy to use or not.
As with the classical and multigenic Laver tables, the ternary Laver tables also produce vivid images. I will post these images soon.