Search found 42 matches

by Mats
August 1st, 2014, 4:54 pm
Forum: Patterns
Topic: New simple methuselah
Replies: 2
Views: 2663

Re: New simple methuselah

It's a variation of Multum in parvo. Generation 7 of this pattern is the same as generation 3 of Multum in parvo.
by Mats
April 27th, 2014, 12:23 pm
Forum: General Discussion
Topic: Generalization of the concept of "spaceship"
Replies: 7
Views: 4654

Re: Generalization of the concept of "spaceship"

Like this?

- A spaceship is a puffer with no smoke.
by Mats
March 14th, 2014, 6:23 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2780
Views: 1131428

Re: Thread For Your Useless Discoveries

A 5x5 methuselah that lasts for 11106 generations.

Code: Select all

x = 5, y = 5, rule = B3/S23
2o$b4o$o3bo$bobo$b2o!
by Mats
March 6th, 2014, 6:48 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2780
Views: 1131428

Re: Thread For Your Useless Discoveries

A 4x4 methuselah that lasts for 4616 generations.

Code: Select all

x = 4, y = 4, rule = B3/S23
3o$2obo$ob2o$bobo!
by Mats
February 10th, 2014, 3:42 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2780
Views: 1131428

Re: Thread For Your Useless Discoveries

"Sketchpad" 12-cell methuselah stabilizes at generation 2564 Probably the longest-lived pattern that fits in a 4x4 square No, it's not the longest-lived pattern to fit in a 4x4 square. Generation 2 of Multum in parvo does and stabilizes at generation 3931. x = 4, y = 4, rule = B3/S23 3o$o2bo$ob2o$3...
by Mats
October 3rd, 2013, 3:33 am
Forum: Patterns
Topic: 4c/83 growing wick (p150)
Replies: 27
Views: 18988

Re: 4c/83 growing wick (p150)

In a news post at pentadeclaton.com a thing called a parasite is desctibed. Link: http://pentadecathlon.com/lifeNews/2011/01/sprouts_and_parasites.html A northeast-directed glider has collided with this stream, causing a messy reaction. It just so happens that the reaction generates another glider, ...
by Mats
September 20th, 2013, 4:10 pm
Forum: Patterns
Topic: Thread For Your Accidental Discoveries
Replies: 1600
Views: 1092192

Re: Thread For Your Accidental Discoveries

EDIT: A quatuor of the ultra-rare beehive at beehive in a symmetrical reaction involving shuttles! x = 19, y = 19, rule = B3/S23 6b2obob2o2$6bo5bo2$7b2ob2o$9bo$obo13bobo$o3bo9bo3bo$4bo4bo4bo$o4bo2bob o2bo4bo$4bo4bo4bo$o3bo9bo3bo$obo13bobo$9bo$7b2ob2o2$6bo5bo2$6b2obob2o! They are no less than 50 tim...
by Mats
July 7th, 2013, 3:13 am
Forum: Patterns
Topic: Thread For Your Accidental Discoveries
Replies: 1600
Views: 1092192

Re: Thread For Your Accidental Discoveries

While trying to find methuselahs in a 10x5 bounding box I found this pattern that not only has a twin hat in its final census, but also exhibits a Pi velocity of (8,10)c/43: x = 10, y = 5, rule = B3/S23 2b3o4bo$bobo5bo$bob2o2bo$2o4b2obo$bo3bo2bo! The same final census in the same number of generati...
by Mats
June 24th, 2013, 2:53 pm
Forum: Patterns
Topic: Blockic Seeds
Replies: 87
Views: 78421

Re: Blockic Seeds

knightlife wrote:For example here is a way to produce an unusual still life with 5 blocks:
It works just as well with 4 blocks:

Code: Select all

x = 21, y = 27, rule = B3/S23
8b2o$8b2o7$7b2o4b2o$7b2o4b2o$2o$2o13$18b3o$18bo$19bo!
It's really a pseudo still life though.
by Mats
May 3rd, 2013, 3:27 am
Forum: General Discussion
Topic: Grid that dies in one step
Replies: 7
Views: 3472

Re: Grid that dies in one step

Here is another (the other?) 9-cell polyplet that dies in one step. x = 5, y = 5, rule = B3/S23 bo$2bobo$b3o$obo$3bo! I know of polyplets with 1, 2, 9, 10, 12 and 14 or more cells that die in one step. Here are examples with 10, 12, 14 and 15 cells. x = 19, y = 18, rule = B3/S23 14bo$2b2o10bo$6o6b4o...
by Mats
April 1st, 2013, 2:15 am
Forum: Other Cellular Automata
Topic: cellular automata
Replies: 8
Views: 3944

Re: cellular automata

For example, imagine that we keep both the initial state in a GOL and a count of the number of iterations. The system is then exactly reversible because when at state n, we can produce state n-1 by restoring the initial state and running forward n-1 steps. To keep a count of the number of iteration...
by Mats
March 31st, 2013, 3:34 am
Forum: Other Cellular Automata
Topic: cellular automata
Replies: 8
Views: 3944

Re: cellular automata

Another way that is simple from a mathematician's point of view, is to use complex numbers (Gaussian Integers) to represent the state of a cell. (or to represent the amplitude of a QM oscillator). Going forwards involved multiplying the state by an imaginary number (and rounding to a Gaussian integ...
by Mats
March 30th, 2013, 2:28 pm
Forum: Other Cellular Automata
Topic: cellular automata
Replies: 8
Views: 3944

Re: cellular automata

It's a pity that the initial post has been deleted. It makes my post appear "out of context", so to say. The question asked was whether time reversible CA:s exist where the state at t+1 is only dependent on the state at time t . In fact an example of a reversible CA where the state at t+1 is depende...
by Mats
March 17th, 2013, 5:19 am
Forum: Other Cellular Automata
Topic: cellular automata
Replies: 8
Views: 3944

Re: reversible cellular automata

For a CA that is only dependent on the state at time t when the state at time t + 1 is computed you have: b(r, t + 1) = F(N(r, t)) If the CA is time reversible you also have: b(r, t - 1) = F(N(r, t)) So b(r, t + 1) = b(r, t - 1) for every t, which leads to N(r, t) = N(r, t - 2) for every t. And that...
by Mats
March 11th, 2013, 6:28 pm
Forum: General Discussion
Topic: Thread For Your Own Theories of CA
Replies: 4
Views: 3184

Re: Thread For Your Own Theories of CA

Here's a hypothesis: A. For all sufficiently large N, there are more N-cell pseudo still lifes than strict still lifes. a1. FASLNTAM N-cell tieless pseudo still lifes than tieless strict still lifes. a2. FASLNTAM N-cell tied pseudo still lifes than tied strict still lifes. B. FASLNTAM N-cell tied s...
by Mats
March 9th, 2013, 5:50 pm
Forum: Patterns
Topic: NEW STILL LIFE & PULSAR
Replies: 2
Views: 2431

Re: NEW STILL LIFE & PULSAR

I'm sorry if I disappoint you but neither the still life nor the pulsar* is new. The still life is an eater 1 found in 1971 and the other one is a pentadecathlon found in 1970. *Normally pulsar refers to this particular object . Objects that return to their original state after two or more generatio...
by Mats
February 21st, 2013, 4:40 pm
Forum: Patterns
Topic: Thread For Your Accidental Discoveries
Replies: 1600
Views: 1092192

Re: Thread For Your Accidental Discoveries

Some time ago I found this polyomino which turns into the same weird still life...

Code: Select all

x = 5, y = 5, rule = B3/S23
2b3o$2bo$3o$obo$2b3o!
by Mats
November 7th, 2012, 3:01 pm
Forum: Patterns
Topic: Thread for your unsure discoveries
Replies: 2092
Views: 1034099

Re: Thread for your unsure discoveries

I found a 10 cell scorpion predecessor. Or probably I rediscovered it...

Code: Select all

x = 6, y = 5, rule = B3/S23
bo$obobo$5bo$2b2obo$3bobo!
by Mats
April 9th, 2011, 6:24 am
Forum: Other Cellular Automata
Topic: Smallest slowest spaceship?
Replies: 27
Views: 18469

Re: Smallest slowest spaceship?

Substitute "a c/4 orthogonal spaceship" for every occurrence of LWSS and it should make more sense. I'm sorry but I'm still having problems understanding your argument. After substitution you get: "the glider's travel is always less than or equal to the c/4 ortogonal spaceship's travel time." In L_...
by Mats
April 9th, 2011, 6:03 am
Forum: Other Cellular Automata
Topic: Smallest slowest spaceship?
Replies: 27
Views: 18469

Re: Smallest slowest spaceship?

IMHO the matter is settled for CGoL: The most appropriate metric is L_1! This is because the proof of the speed limit is based on the fastest possible advance of a diagonal line. Please look up the details in other forum threads. In that sense the glider is as fast as an LWSS. This is simply wrong!...
by Mats
April 9th, 2011, 2:35 am
Forum: Other Cellular Automata
Topic: Smallest slowest spaceship?
Replies: 27
Views: 18469

Re: Smallest slowest spaceship?

quintopia: I'm having trouble following your argument. Is it an argument for L_1 or for L_inf? Or is it a mixture of both? You wrote: "Thus, the glider's travel is always less than or equal to the LWSS's travel time." In L_inf it's "less than" and in L_1 it's "equal". Exactly what do you mean by "al...
by Mats
April 8th, 2011, 4:17 pm
Forum: Other Cellular Automata
Topic: Smallest slowest spaceship?
Replies: 27
Views: 18469

Re: Smallest slowest spaceship?

137ben: I can't see why my sorting is more awkward or more arbitrary than a sorting based on Manhattan metric in a Moore neighbourhood.
by Mats
April 8th, 2011, 2:15 am
Forum: Other Cellular Automata
Topic: Smallest slowest spaceship?
Replies: 27
Views: 18469

Re: Smallest slowest spaceship?

I would like a sorting that is neither L-infinity nor Manhattan metric. Like this: Place the spaceship so that Vx >= Vy. A speed (Vx 1 ,Vy 1 ) > (Vx 2 ,Vy 2 ) iff - Vx 1 > Vx 2 or - Vx 1 = Vx 2 and Vy 1 > Vy 2 This means that a LWSS is faster than a glider. In Manhattan metric they have the same spe...
by Mats
April 1st, 2011, 2:05 am
Forum: Patterns
Topic: Thread For Your Accidental Discoveries
Replies: 1600
Views: 1092192

Re: Thread For Your Accidental Discoveries

Is it worth adding this discovery I made of a parent of the R-pentomino that is five cells and fits in the same sized box as its famous child to the R-pentomino page? The page mentions grandparents and predecessors, but not this parent. x = 3, y = 3, rule = B3/S23 o$bo$3o! All the three grandparent...