3 ms·

Given the fact that, often, in mathematics "things" are elegant, I'm rather curious why achieving a "simple" 2x1 move requires such a complex structure. Is ther

by wiz21c 9y ago

Given the fact that, often, in mathematics "things" are elegant, I'm rather curious why achieving a "simple" 2x1 move requires such a complex structure. Is there an explanation ?

charonn0 9y ago
My understanding is that up til now the existence of a pattern that moves >1 square per generation was only theoretical. https://en.wikipedia.org/wiki/Speed_of_light_(cellular_automaton) https://en.wikipedia.org/wiki/Speed_of_light_(cellular_autom...
- function_seven 9y ago
  It remains a limit. This knightship requires 6 generations to move by 2 units (1 up and 1 diagonal)
- vokep 9y ago
  This moves 2x1 over 6 generations, which is apparently the theoretical minimum, so it does not violate game of life's c. I'm not sure why that is true however, my naive guess is that for any movement forward, some 'reset' action must be taken, so 3 cells forward, 3 reset steps. Otherwise a period 3 knightship should be possible...right?
  - OscarCunningham 9y ago
    >3 cells forward, 3 reset steps Yes, you've got the right idea. It's actually more like "3 preperation steps, 3 steps forward" There's a proof (http://www.njohnston.ca/2009/10/spaceship-speed-limits-in-life-like-cellular-automata/ http://www.njohnston.ca/2009/10/spaceship-speed-limits-in-li...) that a spaceship that travels n cells vertically and m cells horizontally must take at least 2*(n+m) generations to do so.
  - FeepingCreature 9y ago
    Intuitively, I believe that you can't push out more than one adjacent "feeler" per turn, because otherwise the cells behind it would be so dense they'd kill themselves in the next round. So you simply can't get enough density to move more than one step in any given direction per two cycles.
dvgrn 9y ago
Not a simple explanation, I don't think. The size of the smallest spaceship with a given speed and direction is an emergent consequence of iterative rules, so explaining "why" for a Life spaceship is like trying to explain the Seahorse Valley in the Mandelbrot set. In both cases, the iteration rule is simple, but the consequences are complex -- no pun intended.

by wiz21c 9y ago

Given the fact that, often, in mathematics "things" are elegant, I'm rather curious why achieving a "simple" 2x1 move requires such a complex structure. Is there an explanation ?

charonn0 9y ago

My understanding is that up til now the existence of a pattern that moves >1 square per generation was only theoretical. https://en.wikipedia.org/wiki/Speed_of_light_(cellular_automaton) https://en.wikipedia.org/wiki/Speed_of_light_(cellular_autom...

function_seven 9y ago
It remains a limit. This knightship requires 6 generations to move by 2 units (1 up and 1 diagonal)
vokep 9y ago
This moves 2x1 over 6 generations, which is apparently the theoretical minimum, so it does not violate game of life's c. I'm not sure why that is true however, my naive guess is that for any movement forward, some 'reset' action must be taken, so 3 cells forward, 3 reset steps. Otherwise a period 3 knightship should be possible...right?
- OscarCunningham 9y ago
  >3 cells forward, 3 reset steps Yes, you've got the right idea. It's actually more like "3 preperation steps, 3 steps forward" There's a proof (http://www.njohnston.ca/2009/10/spaceship-speed-limits-in-life-like-cellular-automata/ http://www.njohnston.ca/2009/10/spaceship-speed-limits-in-li...) that a spaceship that travels n cells vertically and m cells horizontally must take at least 2*(n+m) generations to do so.
- FeepingCreature 9y ago
  Intuitively, I believe that you can't push out more than one adjacent "feeler" per turn, because otherwise the cells behind it would be so dense they'd kill themselves in the next round. So you simply can't get enough density to move more than one step in any given direction per two cycles.

dvgrn 9y ago

Not a simple explanation, I don't think. The size of the smallest spaceship with a given speed and direction is an emergent consequence of iterative rules, so explaining "why" for a Life spaceship is like trying to explain the Seahorse Valley in the Mandelbrot set. In both cases, the iteration rule is simple, but the consequences are complex -- no pun intended.