Search found 644 matches

by bprentice
September 17th, 2019, 10:05 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

A period 91840 oscillator: x = 81, y = 71, rule = PCA_8 74.2F$73.2F$72.2F$71.2F$70.2F$69.2F$68.2F$67.2F$66.2F$65.2F$64.2F$17. B45.2F$16.F45.2F$15.F45.2F$14.F4.C40.2F$13.F6.C38.2F$12.F8.C36.2F$11. F10.C34.2F$10.F12.C32.2F$9.F14.C30.2F$8.F16.C28.2F$7.F18.C26.2F$6.F 20.C24.2F$5.F22.C22.2F$4.F24.C20.2F$...
by bprentice
September 17th, 2019, 3:42 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

The first splitter in a PCA rule:

Code: Select all

x = 13, y = 8, rule = PCA_8
10.2I$11.2F$10.2A5$2B!
This one splits a domino c/270 diagonal ship into two regular c/270 diagonal ships.

Brian Prentice
by bprentice
September 17th, 2019, 11:11 am
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Do I understand correctly... The rules (PCA_1 thru PCA_8) were inspired by section 2.2 of this paper: http://bprentice.webenet.net/PCA/Two%20Dimensional%208-state%20Triangular%20Reversible%20CA.pdf I believe that they are all reversible but can't prove it. Rules PCA_1 and PCA_5 are definitely rever...
by bprentice
September 16th, 2019, 11:33 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Another reflector demonstration: x = 142, y = 148, rule = PCA_8:T150,150 115.2A3$81.2B3$119.2H5$17.2D3$80.2A$35.2B$30.2A2$22.2A34.2H4$74.2B53. 2H5$53.2A5$64.2H12.2A2$97.2B5$43.2D65.2H3$78.2D16.2H2$22.2A3$71.2B47. 2B$70.2A49.2B5$116.2A$123.2A$75.2B31.2A3$88.2H5.2A$13.2A125.2A$105. 2H2$76.2A$13.2B14.2...
by bprentice
September 15th, 2019, 9:40 am
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

An archive for rule PCA_8 patterns is here: http://bprentice.webenet.net/PCA/PCA_8%20Ships.zip This archive currently contains ships with the speeds tabulated below: Diagonal Ships 2c/2350 DS001.sqc c/270 DS002.sqc 5c/2706 DS003.sqc c/610 DS004.sqc 5c/9370 DS005.sqc 2c/904 DS006.sqc 4c/5688 DS007.sq...
by bprentice
September 14th, 2019, 9:15 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

A PCA_8 reflector demonstration: x = 141, y = 148, rule = PCA_8:T150,150 115.A3$81.B3$119.H5$17.D3$80.A$35.B$30.A2$22.A35.H4$74.B54.H5$53.A5$ 64.H13.A2$97.B5$43.D66.H3$78.D17.H2$22.A3$71.B48.B$70.A50.B5$116.A$ 123.A$75.B32.A3$88.H6.A$13.A126.A$105.H2$76.A$13.B15.B39.H3$4.A3.D2$ 18.B$67.A4$23.A$58.H3...
by bprentice
September 14th, 2019, 1:52 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

A nice period 408 oscillator: x = 119, y = 119, rule = PCA_7 84.I$83.I$82.I$81.I$80.I$79.I$78.I$77.I$76.I$75.I$74.I$73.I$72.I$71. I$70.I$69.I$68.I$67.I$66.I$65.I$64.I$63.I$62.I$61.I$60.I$59.I$58.I$ 57.I$56.I$55.I$54.I$53.I$52.I$51.I$50.I$49.I$48.I$L46.I$.L44.I22.C$ 2.L42.I24.C$3.L40.I26.C$4.L38.I28....
by bprentice
September 14th, 2019, 1:07 pm
Forum: Other Cellular Automata
Topic: Smallest Spaceships Supporting Specific Speeds (5s) Project
Replies: 900
Views: 174826

Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

wildmyron, Thank you for your answer. The exploration of Partitioned Cellular Automata here: http://www.conwaylife.com/forums/viewtopic.php?f=11&t=4098&start=0#p81873 shows that rule PCA_7 has small ships with at least 58 different speeds. These were found in a few hours simply by observing the evol...
by bprentice
September 13th, 2019, 9:06 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Rule PCA_8 /* Put your state count, neighbor count, and function here */ final static int numStates = 16; final static int numNeighbors = 4; private int rule[] = {0,2,4,12,8,10,9,14,1,6,5,7,3,11,13,15}; /* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */ /* order for five neighbors is n,...
by bprentice
September 13th, 2019, 3:28 pm
Forum: Other Cellular Automata
Topic: Smallest Spaceships Supporting Specific Speeds (5s) Project
Replies: 900
Views: 174826

Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

Which rule has the highest number of ships with different speeds in the collection?

Brian Prentice
by bprentice
September 12th, 2019, 8:06 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

A better reflector demonstration: x = 141, y = 146, rule = PCA_7:T150,150 115.A$75.D2$81.H3$119.H8$20.A57.B$35.B$30.A2$22.A39.H50.A$112.A2$112. C$129.H6$70.H2$70.D$61.A$64.B$75.D$97.B2$92.B2$74.A$47.B62.H26.B$138. H$137.C3$22.A$75.B2$120.B$121.B3$81.A2$116.A$123.A$108.A$78.D2$82.D 12.A$13.A126.A$76....
by bprentice
September 12th, 2019, 2:39 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

An archive for rule PCA_7 patterns is here: http://bprentice.webenet.net/PCA/PCA_7%20Ships.zip This archive currently contains ships with 62 different speeds. They are tabulated below: Diagonal Ships 2c/3908 DS001.rle c/1270 DS002.rle 3c/682 DS002.rle c/190 DS004.rle 2c/194 DS005.rle 2c/2208 DS006.r...
by bprentice
September 11th, 2019, 9:22 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

A new PCA rule: /* Put your state count, neighbor count, and function here */ final static int numStates = 16; final static int numNeighbors = 4; private int rule[] = {0,2,4,12,8,5,9,14,1,6,10,7,3,11,13,15}; /* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */ /* order for five neighbors ...
by bprentice
September 11th, 2019, 4:14 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Another PCA_6 oscillator set: x = 14, y = 53, rule = PCA_6 .A$A.B$.A3.D$4.DHD$3.D.D.D12$.A$A.B$.A3.D.D$4.DHDHD$3.D.D.D.D12$.A$ A.B$.A3.D.D.D$4.DHDHDHD$3.D.D.D.D.D12$.A$A.B$.A3.D.D.D.D$4.DHDHDHDH D$3.D.D.D.D.D.D! These have periods of 120, 172, 224 and 276. A larger one with a period of 900: x = 38, ...
by bprentice
September 11th, 2019, 3:09 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Using the technique shown in the post above, five more PCA_4 ships have been found. This brings the total to 41 PCA_4 ships with different speeds. Two diagonal ships with speeds of c/1214 and c/2126: x = 5, y = 4, rule = PCA_4 3.I$2.D.J2$A! x = 4, y = 5, rule = PCA_4 3.H3$C.D$3.E! and three orthogon...
by bprentice
September 11th, 2019, 11:26 am
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Try patterns like this:

Code: Select all

x = 23, y = 22, rule = PCA_4:T150,150
12.A5.G$2.I2.M$8.E2.A$16.N$10.G6.MF$11.M2.K$D15.EF4.O$10.E$2.G5.D2.
K.F7.E$5.I7.D$I.M11.F7.A$ME.J9.A$.B$.D5.M5.I4.F$6.E$7.J3.N$21.J$A$17.
G3.I$5.O7.I$15.F$.I17.B!
Brian Prentice
by bprentice
September 10th, 2019, 10:14 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Some more PCA_6 oscillator sets: x = 69, y = 10, rule = PCA_6 68.J2$46.J19.J2$24.J19.J19.J2$2.J19.J19.J19.J2$B.B17.B.B17.B.B17.B. B$.D19.D19.D19.D! x = 66, y = 6, rule = PCA_6 65.J$44.J19.J$23.J19.J19.J$2.J19.J19.J19.J$.A19.A19.A19.A$J19.J19.J 19.J! Each of these sets has periods 40, 56, 72, 88 ... ...
by bprentice
September 10th, 2019, 9:07 am
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Consider these four PCA_6 oscillators: x = 11, y = 74, rule = PCA_6 .B.B$D.D.D23$.B.B.B$D.D.D.D23$.B.B.B.B$D.D.D.D.D23$.B.B.B.B.B$D.D.D .D.D.D! They have periods of 408, 16300, 534012 and 5147120. Now consider this pattern: x = 61, y = 2, rule = PCA_6 .B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B...
by bprentice
September 9th, 2019, 11:07 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Another PCA rule: /* Put your state count, neighbor count, and function here */ final static int numStates = 16; final static int numNeighbors = 4; private int rule[] = {0,2,4,3,8,10,6,14,1,9,5,7,12,11,13,15}; /* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */ /* order for five neighbor...
by bprentice
September 8th, 2019, 11:31 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Continuing the exploration of rule PCA_3, some symmetrical patterns generate ships constructed of dominoes: x = 31, y = 32, rule = PCA_3 15.A$14.B2A$13.A2B2A$12.B2A2B2A$11.A2B2A2B2A$10.B2A2B2A2B2A$9.A2B2A 2B2A2B2A$8.B2A2B2A2B2A2B2A$7.A2B2A2B2A2B2A2B2A$6.B2A2B2A2B2A2B2A2B2A $5.A2B2A2B2A2B2A2B2A2B2A$4...
by bprentice
September 7th, 2019, 9:36 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Four more PCA_3 patterns. Two new diagonal ships with periods 3c/642 and c/2188: x = 5, y = 3, rule = PCA_3 3.H$D3.D$.B.E! x = 5, y = 4, rule = PCA_3 3.A$H$.H.D$2.A.D! The archive at: http://bprentice.webenet.net/PCA/PCA_3%20Ships.zip now contains ships with these speeds: c/11 S008.sqc c/12 DS001.sq...
by bprentice
September 6th, 2019, 7:11 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Another Golly rule tree: /* Put your state count, neighbor count, and function here */ final static int numStates = 16; final static int numNeighbors = 4; private int rule[] = {0,4,8,3,1,10,6,11,2,9,5,13,12,14,7,15}; /* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */ /* order for five n...
by bprentice
September 5th, 2019, 10:56 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

Two PCA_2 oscillators with periods 501 and 2004: x = 77, y = 32, rule = PCA_2 15.AB43.AB$15.HD43.HD2$13.I$14.I9$28.C44.C$27.C44.C$AB28.AB13.AB28. AB$HD28.HD13.HD28.HD$4.L$3.L9$17.F$18.F2$15.AB43.AB$15.HD43.HD! Two more with periods 489 and 1956. x = 73, y = 30, rule = PCA_2 14.AB41.AB$14.HD41.HD2$12...
by bprentice
September 5th, 2019, 1:46 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

The Square Cell version of PCA is here: http://bprentice.webenet.net/PCA/PCA.zip A dialog can be used to display and change the rule table allowing exploration of other rule variants. Patterns are rotated correctly which makes pattern editing easier. The paper here: http://bprentice.webenet.net/PCA/...
by bprentice
September 3rd, 2019, 11:47 pm
Forum: Other Cellular Automata
Topic: Partitioned Cellular Automata
Replies: 101
Views: 14048

Re: Partitioned Cellular Automata

AforAmpere

I will add your new ships to the list and archive tomorrow.

Hdjensofjfnen

Your ship is included, it has a period of 7c/13549.

Brian Prentice