Alexis-
Nice going! Amazing - I had no idea that this type of sequence had
been previously studied, and it turns out to be something useful to
boot. I feel better now that you have finally identified it as
the "Gray Code"... and what a cool name, too. When I discovered the
first cyclic trinary cell and then plugged one cell into another cell
to create multiple trits, I found it confusing at first, and knew
that it was a little weird since only one digit changed at a time,
but I have always just attributed the reading of the digits as having
a dependency on the other digits ("digit dependency"). This is true,
of course, but nonspecific and I never thought to study it further.
However, I still find it amazing that changing the digits one at a
time can cycle throught the same number of states as a binary or
decimal type counter.
Also, I guess, it's no accident that LT counters use the gray code,
since they are virtual mechanical devices:
"Definition: An ordering of 2n binary numbers such that only one bit
changes from one entry to the next...
...Note: Gray codes are particularly useful in mechanical encoders
since a slight change in position only affects one bit."
(http://www.nist.gov/dads/HTML/graycode.html)
So, there is a gray encoded number for every n-ary number, for
example in binary:
"Decimal / Gray code / Binary
0 0000 0000
1 0001 0001
2 0011 0010
3 0010 0011
4 0110 0100
5 0111 0101
6 0101 0110
7 0100 0111
8 1100 1000
9 1101 1001
10 1111 1010
11 1110 1011
12 1010 1100
13 1011 1101
14 1001 1110
15 1000 1111"
(http://yagni.com/graycode/)
there's a discussion at the end that talks about the "digit
dependency" in reading gray code and conversion to and from binary.
-Steve
Nice going! Amazing - I had no idea that this type of sequence had
been previously studied, and it turns out to be something useful to
boot. I feel better now that you have finally identified it as
the "Gray Code"... and what a cool name, too. When I discovered the
first cyclic trinary cell and then plugged one cell into another cell
to create multiple trits, I found it confusing at first, and knew
that it was a little weird since only one digit changed at a time,
but I have always just attributed the reading of the digits as having
a dependency on the other digits ("digit dependency"). This is true,
of course, but nonspecific and I never thought to study it further.
However, I still find it amazing that changing the digits one at a
time can cycle throught the same number of states as a binary or
decimal type counter.
Also, I guess, it's no accident that LT counters use the gray code,
since they are virtual mechanical devices:
"Definition: An ordering of 2n binary numbers such that only one bit
changes from one entry to the next...
...Note: Gray codes are particularly useful in mechanical encoders
since a slight change in position only affects one bit."
(http://www.nist.gov/dads/HTML/graycode.html)
So, there is a gray encoded number for every n-ary number, for
example in binary:
"Decimal / Gray code / Binary
0 0000 0000
1 0001 0001
2 0011 0010
3 0010 0011
4 0110 0100
5 0111 0101
6 0101 0110
7 0100 0111
8 1100 1000
9 1101 1001
10 1111 1010
11 1110 1011
12 1010 1100
13 1011 1101
14 1001 1110
15 1000 1111"
(http://yagni.com/graycode/)
there's a discussion at the end that talks about the "digit
dependency" in reading gray code and conversion to and from binary.
-Steve