~ isle ex ~ |
HOME | MAP | NEW | CONTACT |

## Transmusical Experiments Reference## Table I - Musification Parameters
## Table II - Cellular Automaton Rules
## Notes1. Rule Group
**BOT**- "Binary outer totalistic". These are counting rules. The number of 1-valued neighbors are tallied up and the next value of the center cell depends on its last value and this neighbor count. "Outer" totalistic rules distinguish the center cell in this way from the other cells in the neighborhood. In my own rule-definition scheme, any binary rule can have "decay", which means that when a cell goes from 1 to 0 it passes through C - 2 intermediate states, one at each CA step. Note that these decay states are "refractory" -- that is, a cell has to cycle back to 0 before it can be "turned on" again as per the look-up table. This scheme allows us to obtain a plethora of interesting nonbinary rules from a binary table, by merely parameterizing C.
**GB**- "General binary". This group encompasses all possible
binary rules for a given neighborhood. As such, it includes the BOT rules,
but would be a more cumbersome way to specify them. So the interest here
is of course in non-BOT rules -- rules where not all neighbors are
created equal, so to speak. Where, for instance, the rule distinguishes
opposite from adjacent neighbors or North neighbors from South ones. There
are an immense number of GB rules. For 5-hoods there are
2
^{32}(> 4 billion) unique lookup table configurations, while for 9-hoods the number explodes to a staggering 2^{512}(> 10^{154}). Moreover, we can, as with BOT rules, further expand the number of rules by simply specifying values for C greater than 2, with the understanding that the additional states are refractory decay states. **Cyclic**- This group, as implemented elsewhere on Isle Ex, goes beyond the "classic" C-parameterized H5T1 Cyclic CA to also parameterize H and T, where T (the "threshold") is the minimum number of superior neighbors necessary to trigger promotion.
2. H ("hoodsize"). Each CA rule showcased on Isle Ex
uses one or the other of the following
cell "neighborhoods", where the N's are the neighbors of cell X. Since
the neighborhood consists of all cells which might influence the value
of X at the next step (via the CA rule), it includes X itself. Thus
at Isle Ex, H is always either 5 or 9.
von Neumann neighborhood Moore neighborhood N N N N N X N N X N N N N N 3. C ("cellsize"). This is simply the number of possible cell values,
which are normally numbered 0 to C - 1.
**BOT rules**-
The encoding used is the one
published in Stephen Wolfram's article,
"Two-Dimensional Cellular Automata".
(Note: A few of the codes specified in Wolfram's paper seem to be
misprints. For instance, some codes in the captions to Figures 7
and 9 exceed what I take to be the largest possible value for a 9-cell code,
2
^{18}- 1 = 262143, which denotes a table with all bits set. The code 174766 appears to generate the pattern depicted in Figure 7(e); I haven't attempted to correct any others.) **GB/H=5 rules**- As with BOT rules, the GB code is obtained by packing the lookup table bits into a numerical value, this time in hexadecimal format for the sake of compactness. The ordering of the table entries is that provided by an ascending walkthrough of the neighborhood states, where the cell states are mapped to the table index bits as follows (from high bit to low bit): E W S N C. As for the packing order of the table entries in the code, the table index is mapped directly to code bit-significance. My neighbor-ordering is the same as that given in the book Cellular Automata Machines by Tommaso Toffoli and Norman Margolus, but my packing order is opposite to that used in their code examples on page 33. (BTW, their code for the Parity rule is in error - binary 1001 is hex digit 9, not D. So using their packing order the code should be 69969669.) My ascending bit-significance packing order makes the GB code consistent with the BOT code.
## Table III - CA Demographics
Page contents created 4-Feb-1998. See map for file modification date. |