Serizawa

[12Glider]

Post patterns you have found in the rule Serizawa here.
p30 gun:

Code: Select all

x = 20, y = 20, rule = Serizawa
6.A7.A4$5.A7.A.A$19.A$5.A8.B$13.A.A4$5.A.A$6.B8.A$A18.A$5.A.A7.A5$6.A
7.A!

[flipper77]

Here's a p3 and p4 oscillator:

Code: Select all

x = 5, y = 14, rule = Serizawa
2.B$.BA$2.B10$4.B$B!

Here's a dirty rake:

Code: Select all

x = 9, y = 11, rule = Serizawa
2.A$7.B$.A2.A.A.B$7.B$2.A4.B$A7.B$7.A3$2.A.A$3.B!

Here's some puffers:

Code: Select all

x = 70, y = 7, rule = Serizawa
7.A2.A$.A4.AB2ABA$ABA9.A4.A17.A2.A20.A4.A2.A$A.A5.2A.A.A2.ABA10.A4.AB
2ABA18.ABA2.AB2ABA$7.A2.A.A3.A.A9.ABA4.B4.A17.A.A3.B4.A$10.ABA15.A.A
5.2A.A25.2A.A$12.A22.A28.A!

And finally, here's a rake:

Code: Select all

x = 7, y = 6, rule = Serizawa
4.A$3.ABA$3.A.A$A.2AB.A$ABA2.B$.A!

Most of these patterns I found popped up naturally, and messed around with some of them.

[12Glider]

Here's a p3 and p4 oscillator

The "p4" is actually a p10.

[flipper77]

Thanks for catching that, I was working, and I quickly pasted in my patterns without checking.

[knightlife]

Three cell infinite growth:

Code: Select all

x = 3, y = 4, rule = Serizawa
.B3$B.B!

Dirty puffers cleanup each other:

Code: Select all

x = 24, y = 8, rule = Serizawa
.B2.B$A.2B.B$4.3A$5.A$18.B2.B$17.A.2B.B$21.3A$22.A!

Horizontal spacing can be changed with similar results:

Code: Select all

x = 15, y = 8, rule = Serizawa
.B2.B$A.2B.B$4.3A$5.A$9.B2.B$8.A.2B.B$12.3A$13.A!

A couplle of puffers with clean output:

Code: Select all

x = 59, y = 8, rule = Serizawa
11.A2.A$10.AB2ABA$2.A2.A4.A5.A26.A2.A6.A2.A$.AB2ABA4.3A.A26.AB2ABA4.A
B2ABA$A5.BA33.A5.BA2.AB5.A$.A.2A37.A.3A6.3A.A2$46.A6.A!

p10 backrake:

Code: Select all

x = 33, y = 13, rule = Serizawa
3B15.B.3B$B17.B.B.B$3B15.B.B.B$B.B15.B.B.B$3B15.B.3B3$11.A14.A$7.B2.A
BA12.ABA2.A$6.A.B2A.A12.A.A.ABA$7.A.A18.A3.A$7.ABA17.2A2.A$8.A19.A!

flipper77 posted the p6 earlier.

[p46beth]

p24 double rake:

Code: Select all

x = 15, y = 17, rule = serizawa
5.B3.B$4.A.3A.A2$5.A3.A$.B2.3A.3A2.B$A.A2.5A2.A.A$4.B.A.A.B$4.A5.A$3.
2A2.A2.2A$2.4A.B.4A$3.2A5.2A2$6.A.A$5.A3BA$6.3A2$7.A!

[12Glider]

That's a sick rake you have there.

[Extrementhusiast]

P24 eight-barreled rake:

Code: Select all

x = 48, y = 17, rule = Serizawa
41.A$39.2A.A3.A$34.A3.A2.A5.B$9.2A22.ABA3.4A.A.A$8.AB3.A6.B11.AB3.A3.
A2.3A$9.2A8.A.B.A9.A3.ABAB3.A.A$12.A9.AB3A9.B.2A.B5.B$2.A6.2A6.2A.AB
5.A5.A.A8.A.A$A7.AB2.A4.AB3.A.AB3A3.AB2.B3.A3.3A$2.A6.2A6.2A.AB5.A5.A
.A8.A.A$12.A9.AB3A9.B.2A.B5.B$9.2A8.A.B.A9.A3.ABAB3.A.A$8.AB3.A6.B11.
AB3.A3.A2.3A$9.2A22.ABA3.4A.A.A$34.A3.A2.A5.B$39.2A.A3.A$41.A!

[p46beth]

A p60 agar:

Code: Select all

x = 243, y = 249, rule = Serizawa
.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.
A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.
A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.
A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.
A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.
A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.
A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.
A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.
A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.
A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A
.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$
.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.
B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.
A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.
A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.
A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.
B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.
A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A6$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A
.A13.A.A13.A.A13.A.A13.A.A13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B15.B8$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
15.B15.B15.B15.B15.B15.B$A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.
A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A6$A.A13.A.A13.A.A13.
A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A13.A.A
13.A.A$.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B15.B
!

Just one unit cell of the agar on a 16 by 16 torus:

Code: Select all

x = 16, y = 16, rule = Serizawa:T16,16
.B$A.A6$A.A$.B!

By spacing the gliders, arbitrarily large period agars can be made.

[Extrementhusiast]

A p60 agar:

Code: Select all

(pattern)

That looks like a Maltese cross!

[cloudy197]

Here's a simpler way to control a construction arm using only one block and no more than 4 gliders on each operation:

Code: Select all

x = 27, y = 42, rule = Serizawa
.A10.A10.A3$11.B10.B$10.A.A8.A.A2$3.B11.B$2.A.A9.A.A8.A$24.ABA$24.A.A
4$.B$A.A7$.A10.A3$2.B8.B$.A.A6.A.A2.A$14.ABA$14.A.A$4.A$3.ABA$3.A.A5.
B$10.A.A2$14.B$5.B7.A.A$4.A.A5$.B$A.A!

[ebcube]

Great ones, cloudy. I just found one to move a red cell four blocks left or right:

Code: Select all

x = 7, y = 18, rule = Serizawa
2.A11$.B$A.A2.B$4.A.A2$3.A$2.ABA$2.A.A!

And another one to move it five blocks (unfortunately, this one needs five gliders). Using both, you can move a cell wherever you want.

Code: Select all

x = 8, y = 26, rule = Serizawa
2.A14$.B$A.A$6.B$5.A.A$2.B$.A.A$6.B$5.A.A3$.B$A.A!

And an easier one to move it just one block to the side:

Code: Select all

x = 9, y = 12, rule = Serizawa
2.A4$.B$A.A$5.B$4.A.A3$7.B$6.A.A!

[cloudy197]

Tight salvos of gliders can be created using this reaction:

Code: Select all

x = 42, y = 37, rule = Serizawa
23.A$24.B$23.A$40.2A$A12.2A24.AB$.B12.BA24.2A$A12.2A17$31.A$30.ABA$
30.A.A4$32.B$31.A.A5$28.B$27.A.A!

[knightlife]

Improved "5 to the right" needs only three gliders:

Code: Select all

x = 28, y = 26, rule = Serizawa
2.A19.A14$.B19.B$A.A17.A.A$6.B19.B$5.A.A17.A.A$2.B$.A.A$6.B$5.A.A17.B
$24.A.A2$.B$A.A!

The two leading gliders are in the same positions.

Simple systematic way to retract arm by any amount 5 cells or more with only three gliders:

Code: Select all

x = 71, y = 18, rule = Serizawa
4.A29.A29.A7$3.B29.B29.B$2.A.A27.A.A27.A.A4$.B$A.A6.B29.B29.B$8.A.A
20.B6.A.A27.A.A$30.A.A$61.B$60.A.A!

Leftmost glider moves down two cells to retract arm by one additional cell.
Rightmost glider can be removed if arm is supposed to fire a glider as well.

Found a "bomber" that can interact with another one to create quadratic growth:

Code: Select all

x = 29, y = 15, rule = Serizawa
5.A2.A$.B2.AB2ABA2.B$A.A.AB2.BA.A.A$6.2A8$20.A2.A$16.B2.AB2ABA2.B$15.
A.A.AB2.BA.A.A$21.2A!

Another quadratic (settles after 2K to 3K generations):

Code: Select all

x = 23, y = 3, rule = Serizawa
.A3.A3.A3.A3.A3.A$ABA.ABA.ABA.ABA.ABA.ABA$A5.A.A5.A.A5.A!

[p46beth]

I have been trying to determine the end behavior of this rule, modeled with very large toroidal universes. I have run a bunch of tori of sizes 8192 by 8192, 4096 by 4096, and 16384 by 16384, each starting with random-fill (50%). (I have been doing this for several other rules, but my results for those are not as complete as for serizawa). The results for serizawa are nothing spectacular: Almost all of the universe is covered with single cell still-lives. There are a few p3s, and a few p10s. I am skeptical that anything else (or at least any other still life/oscillators) will occur naturally with any significant frequency.
The average density is about .0050. However, this might change for other starting densities. I will do searches on other starting conditions and see what final densities turn up.

EDIT: I found a tagalong for a glider:

Code: Select all

x = 6, y = 6, rule = Serizawa
.A$B$.A2.A$3.A.A$2.AB$3.2A!

[p46beth]

I know there is already a Serizawa thread, but I think this deserves a thread of its own [Note from Nathan: I merged with the Serizawa thread]. I was searching for 1d infinite growth patterns, and found the following:

Code: Select all

x = 22, y = 50, rule = serizawa
6.3BA2.A2B16$7.4A2BA13$6.2BA2.A2B9$A3.B.A7.2B4.AB11$5.B3.A2BA2.BAB.A!

This motivated me to search for smaller patterns, and eventually, I found a 1 by 4 pattern with infinite growth!

Code: Select all

x = 4, y = 1, rule = Serizawa
A2BA!

At this point, I did an exhaustive search, and found that no pattern in a 1 by 3 box exhibits infinite growth, and only one pattern in a 1 by 4 box does.

Following this, I did a complete search of the 2 by 3 box, and found that no 2 by 3 pattern exhibits infinite growth. Thus, the only bounding box left to check is the 3 by 3, at which point the bounding box question will be fully answered.
EDIT: knightlife has found infinite growth patterns in a 3 by 3 box, completing the question!

But, as I've said on (several) other threads, I find bounding box to be one of the less natural measurements of pattern size. In the way of minimum population, a 3 cell infinite growth pattern was found on the other thread:

Code: Select all

x = 3, y = 4, rule = Serizawa
.B3$B.B!

I did a complete search of 2-cell patterns, and none of them exhibit infinite growth, so that question is answered.

Another way of classifying pattern size is by using the minimum p such that the pattern is completely contained in a p-neighborhood (using the metric induced by the CA neighborhood). For the Moore neighborhood, this translates into bounding square, so I'll admit that for rules in the Moore neighborhood the bounding box has some merit.
For the JvN neighborhood, a radius 1 neighborhood would be the plus-pentomino. I did a complete search, and found no infinite growth patterns which fit in a plus. Since the 1 by 4 pattern fits in a radius 2 neighborhood, this establishes the minimum radius of a pattern with infinite growth.

Lastly, we have the bounding-polyomino. Any triomino fits inside a 2 by 3 box, so no pattern with a bounding triomino can exhibit infinite growth. And of course, the 1 by 4 pattern has a bounding polyomino of 4, so this is in fact the minimum.

[knightlife]

A p18 oscillator that is really a six-barrel p18 gun with blocked output:

Code: Select all

x = 12, y = 13, rule = Serizawa
4.A2.A5$4.B3.A$A2.B7.A$4.B3.A5$4.A2.A!

Any or all of the six outermost cells can be removed to provide up to six p18 glider streams.

[p46beth]

Cool. Any ideas on how best to do a complete search of 3x3 patterns which might exhibit infinite growth?

[knightlife]

Just 4 cells produces three different spaceships traveling North:

Code: Select all

x = 6, y = 8, rule = Serizawa
B.B3$5.B4$5.B!

The largest spaceship has 8 phases.

[12Glider]

I have been trying to determine the end behavior of this rule, modeled with very large toroidal universes. I have run a bunch of tori of sizes 8192 by 8192, 4096 by 4096, and 16384 by 16384, each starting with random-fill (50%). (I have been doing this for several other rules, but my results for those are not as complete as for serizawa). The results for serizawa are nothing spectacular: Almost all of the universe is covered with single cell still-lives. There are a few p3s, and a few p10s. I am skeptical that anything else (or at least any other still life/oscillators) will occur naturally with any significant frequency.
The average density is about .0050. However, this might change for other starting densities. I will do searches on other starting conditions and see what final densities turn up.

EDIT: I found a tagalong for a glider:

Code: Select all

x = 6, y = 6, rule = Serizawa
.A$B$.A2.A$3.A.A$2.AB$3.2A!

The proposed tagalong is a glider itself.

[knightlife]

Cool. Any ideas on how best to do a complete search of 3x3 patterns which might exhibit infinite growth?

Even though there are 3^9 = 19683 (EDIT: corrected value) starting patterns for 3x3 it should not take too long to do an exhaustive search with a Python script on a fast desktop PC. The hard part is to test for infinite growth reliably. Other than eliminating starting patterns with population less than three, it may not even be worth checking for reflections and rotations. The job can still be done in reasonable time as follows:

1) track maximum population at each tic.
2) check for minimum growth (a new max population within max_tics generations).
3) stop checking for infinite growth if max_gens is reached.
4) if population is still growing when max_gens is reached then save pattern for verification.

max_tics = 1000 should be overkill (knowing Serizawa, 100 is probably enough, reducing run time)
max_gens = 10000 is probably OK, although it is tough to find a small methuselah that lasts even 1000 tics.

My Python skills are pretty lean, but the task is simple enough I will try to do this.
I have been wanting to do automated searches for some time. Suggestions are welcome.
I have a feeling the search will come up empty for infinite growth, in which case I will search for methuselahs.

If anyone posts a Golly script for an automated search using Python, that would flatten the learning curve a lot.
I suspect there is someone reading this who could whip this out in no-time.

Code: Select all

x = 3, y = 3, rule = serizawa
2B$AB$B.B!

[knightlife]

I had some success in the search for Serizawa 3x3 infinite growth patterns:

Code: Select all

x = 3, y = 3, rule = serizawa
B.A$.BA$B.A!

I have not done an exhaustive search yet, but I found candidates to investigate.
These are the early results. I have to eat my words about an empty search!
Here is a three cell pattern with infinite growth:

Code: Select all

x = 3, y = 3, rule = serizawa
B.B2$A!

This beats the previously posted 3-cell pattern that has a 3x4 bounding box

[p46beth]

Congratulations! Now the question of minimal bounding boxes for infinite growth patterns is fully answered, along with minimum bounding polyominio, population, and p-neighborhood.

Next challenge: to find the minimum population/bounding p-neighborhood/bounding box/bounding polyomino for a pattern with quadratic growth.

[knightlife]

How about 1-cell wide patterns with infinite growth?
I have found the smallest such pattern, a 4-cell polyomino:

Code: Select all

x = 4, y = 1, rule = serizawa
A2BA!

Other larger infinite growth 1-cell wide patterns tend to have this one as a subset.

[ssaamm]

What about this 3-cell rake parent?

x = 3, y = 3, rule = serizawa
2.A2$B.B!

EDIT: I should have looked harder; This was already discovered