i think not just math lovers - these kinds of levels should appeal to
many people including clockmakers, computer geeks, mechanical
engineers, and artists. indeed, donald has expanded the technique
introduced by alexis last month to include all bases up to base-8.
there's also a new similar multi-base sliding mirror technique i
found that goes from base 2 up to base 13. each cell pulses the next
to make it progress automatically.
see also (at last) the new compact quinary cell introduced in special-
no-lpb using rotary mirrors that makes the most moves yet:
27-Quint Quinary Counter (Base 5)
(3/2) x 3^3 x 5^27 x (2 x 5) + (2 moves to flag)
= (3 thousand million million million moves)
= 3 x 10^21
= 3 017 485 141 754 150 390 627
(Trinary Counter I: 94 143 178 829)
as well, there's a complex new type of array of interacting rotary
mirrors that i have (almost) completely figured out that gives all
the odd numbered bases (only limited by the size of the 16x16 playing
field). this means that all bases are now available by combining with
a binary divider. the new method is pretty cool to watch at high
bases as a cell gets worked over cyclicly from each end in an in-one-
end-and-out-the-other kind-of way. the max is around a couple hundred
pulses, or about 400 before a complete recycling of a large array. i
suspect some folks (including me) have been looking for this for
quite a while, maybe especially those who use the technique of
densely packed array of rotating mirrors (which has, stubbornly,
never cycled).
to summarize, (it's 75% done):
cell type: 2A 2A,1B 2A,2B ABC?????
# mirrors 4m+1 4m-1 4m-3 4m+1 ?
0 1
1 3 7 ?
2 9 5
3 11 15 ?
4 17 13
5 19 23 ?
6 25 21
7 27 31 ?
8 33 29
9 35 39 ?
10 41 37
11 43 47 ?
12 49 45
�& �& �& �& �&
and so on�&
maybe someone else can find the missing 25% peice of the puzzle if it
exists - (please let me know if you do). the symmetry properties may
prohibit the 4th class of bases - that would be a shame as it would
leave an ugly gap.
there's more to come - these other 3 things were by-products as i was
working on an idea about chaotic order, but the order kept popping
out, leaving the chaos behind.
-steve
ps yono,
i failed your pop-quiz - i will have to re-take it.
-S
many people including clockmakers, computer geeks, mechanical
engineers, and artists. indeed, donald has expanded the technique
introduced by alexis last month to include all bases up to base-8.
there's also a new similar multi-base sliding mirror technique i
found that goes from base 2 up to base 13. each cell pulses the next
to make it progress automatically.
see also (at last) the new compact quinary cell introduced in special-
no-lpb using rotary mirrors that makes the most moves yet:
27-Quint Quinary Counter (Base 5)
(3/2) x 3^3 x 5^27 x (2 x 5) + (2 moves to flag)
= (3 thousand million million million moves)
= 3 x 10^21
= 3 017 485 141 754 150 390 627
(Trinary Counter I: 94 143 178 829)
as well, there's a complex new type of array of interacting rotary
mirrors that i have (almost) completely figured out that gives all
the odd numbered bases (only limited by the size of the 16x16 playing
field). this means that all bases are now available by combining with
a binary divider. the new method is pretty cool to watch at high
bases as a cell gets worked over cyclicly from each end in an in-one-
end-and-out-the-other kind-of way. the max is around a couple hundred
pulses, or about 400 before a complete recycling of a large array. i
suspect some folks (including me) have been looking for this for
quite a while, maybe especially those who use the technique of
densely packed array of rotating mirrors (which has, stubbornly,
never cycled).
to summarize, (it's 75% done):
cell type: 2A 2A,1B 2A,2B ABC?????
# mirrors 4m+1 4m-1 4m-3 4m+1 ?
0 1
1 3 7 ?
2 9 5
3 11 15 ?
4 17 13
5 19 23 ?
6 25 21
7 27 31 ?
8 33 29
9 35 39 ?
10 41 37
11 43 47 ?
12 49 45
�& �& �& �& �&
and so on�&
maybe someone else can find the missing 25% peice of the puzzle if it
exists - (please let me know if you do). the symmetry properties may
prohibit the 4th class of bases - that would be a shame as it would
leave an ugly gap.
there's more to come - these other 3 things were by-products as i was
working on an idea about chaotic order, but the order kept popping
out, leaving the chaos behind.
-steve
ps yono,
i failed your pop-quiz - i will have to re-take it.
-S