Reversible Wireless World

[alexv]

Hello

I found only a few threads about reversible CA here, maybe attached CA could be interesting.
It is so-called second-order reversible CA with four states produced from CA with two states.
Simple stable gliders -- are three-cell "ants" moving in vertical and horizontal directions with
unit speed with reflections, collisions and splitting. The ants can be used for construction
of different kinds of "wireless circuits." Some examples are in attachment (zip, Golly format).
Four slightly different rules are there: WlAnt, WlAnt-2,WlAnt-3,WlAnt-4. All examples use
WlAnt rule. Most "wireless circuits" work with all rules in the same way.

Here is a description of a rule (from readme.txt)
-------------------------------------------
Rule WlAnt:

There are four states: 0 (empty, white), 1 (red), 2 (green), 3 (blue).

A cell with state 0 or 2 (white or green) is called "even"
and a cell with state 1 or 3 (red or blue) is called "odd"

A step may be divided into two stages:

First stage:
Mark all cells satisfying two conditions:
(1) total number of odd cells in four closest positions (up, down, left, right) is one or two,
(2) cells in four diagonal positions are even.

Second stage:
For unmarked: exchange red and green cells (1<->2).
For marked cells: change empty into red, red into blue, blue into green,
green into empty (0->1->3->2->0).

UPDATE Mar 6: WlAntWorldNews.zip with 32 new patterns discussed in the thread

[Sphenocorona]

I managed to make a signal generator:

Code: Select all

x = 13, y = 20, rule = WlAnt
4.2C3.2C$4.2C3.2C$3.3C3.2C$3.3C3.2C$9.2C$2C8.2C$2C8.2C$2C3.2C3.2C$2C
3.2C3.2C$2C9.2C$2C9.2C$2C9.2C$5.3C3.2C$5.3C3.2C$2C9.2C$2C9.2C$11.2C$
3.2C.A.2C$3.2C.C.2C$6.B!

[bprentice]

Here are three more:

Code: Select all

x = 18, y = 50, rule = WlAnt
11.4C$11.4C2$8.2C6.2C$8.2C6.2C$8.2C$8.2C.ACB.BCA2$11.3C$11.3C7$11.4C
$11.4C2$8.2C2.BCA.2C$8.2C6.2C$8.2C$8.2C.ACB.BCA2$11.3C$11.3C7$3.2C8.
2C$3.2C8.2C2$2C2.BCA3.BCA3.2C$2C12.B.2C$3.A10.C$3.C10.A$3.B3$14.B$3.
A10.C$3.C10.A$2C.B$2C3.ACB3.ACB.BCA2$3.2C7.2C$3.2C7.2C!

Brian Prentice

[alexv]

Additional generated signals may be "collected" sometimes (see WlAnt-split.rle), but I did not guess yet if it is possible for examples like above.

[alexv]

The generator - collector pair for the first bprentice example.

Code: Select all

x = 49, y = 10, rule = WlAnt
3.4C35.4C$3.4C35.4C2$2C6.2C29.2C6.2C$2C6.2C29.2C6.2C$2C45.2C$2C.ACB.B
CA13.BCA13.BCA.ACB.2C2$3.3C37.3C$3.3C37.3C!

I think, it may be done also for any similar examples (CA is reversible, after all)

[bprentice]

An extension of the Wireless Ant Program is included in the following archive:

http://bprentice.webenet.net/Java%20Squ ... 0World.zip

This extension adds diagonal moving ants to the orthogonal moving ants by increasing the number of states to 7. The program extends my basic Square Cell program which is briefly described in the file "Java Square Cell.html" which is included in the archive. The Java source code together with some example oscillators and guns are also included.

Brian Prentice

[alexv]

Brian

If your extension reversible? Initial CA was also used for research of reversible circuits (aka conservative billiard ball logic). In fact, due to example with Fredkin gate it is computationally universal reversible CA.

[alexv]

Some links with additional information about discussed CA

Initial definition: http://ayvlasov.wordpress.com/2012/07/23/qu-ants/
Computational universality: http://quantumbot.wordpress.com/2013/08 ... nto-logic/
Penrose tiling (an analogue of WlAnt-4): http://ayvlasov.wordpress.com/2012/09/27/penroses-ants/

[alexv]

Signal generator suggested by Sphenocorona has a difference with other generators mentioned above, because
it may be turned on by external signal. Simpler example of such generator is

Code: Select all

x = 14, y = 13, rule = WlAnt
3.2C4.3C$2.3C4.3C$2.2C3$7.2C$BCA4.2C$7.2C3$2.2C8.2C$2.3C6.3C$3.2C6.2C
!

It is not clear how to create "true" collector for such a case. Yet, there is another simple model with
possibility to prevent infinite activity using second signal to turn it off

Code: Select all

x = 81, y = 16, rule = WlAnt
70.2C4.3C$69.3C4.3C$69.2C3$74.2C$68.BCA3.2C$74.2C$69.2C$69.2C2$BCA2$
69.2C8.2C$69.3C6.3C$70.2C6.2C!

[bprentice]

Is your extension reversible?

I think so. Here are some more simple guns:

Code: Select all

x = 10, y = 10, rule =WlAnt
3.2C$3.2C2$.ACBCA2.2C$8.2C$2C$2C2$5.2C$5.2C!

Code: Select all

x = 18, y = 25, rule = WlAnt
.C$2C5$7.C$6.3C$7.C15$15.3C$16.C!

Code: Select all

x = 2, y = 31, rule = WlAnt
2C$2C$.C2$.B$.C$.A2$.B$.C$.A2$.B$.C$.A2$.A$.C$.B2$.A$.C$.B2$.A$.C$.
B2$.C$2C$2C!

Brian Prentice

[alexv]

Brian

Did you check possibility to inverse evolution for patterns with interaction between
usual and diagonal ants?

[bprentice]

Did you check possibility to inverse evolution for patterns with interaction between
usual and diagonal ants?

I had not checked that situation. I now agree that my extension to your program is not reversible. Thank you for pointing that out Shura.

Brian

[alexv]

Brian

Anyway your ideas look interesting, because such reversible automata with 7 states indeed should exist.
Formally, second order automata should have 3x3=9 states, but two states may be omitted sometimes.
I have got very similar CA modeling signals 0 and 1 by two different kinds of ants.
Here is rule AntBitS7.rule (with icons)

Code: Select all

@RULE AntBitS7

@TREE

num_states=7
num_neighbors=8
num_nodes=28
1 0 3 6 1 4 5 2
1 1 4 5 0 3 6 2
1 2 4 5 1 3 6 0
2 0 1 2 0 1 2 0
2 1 1 0 1 1 0 1
2 2 0 2 2 0 2 2
2 1 0 0 1 0 0 1
2 0 0 0 0 0 0 0
2 2 0 0 2 0 0 2
3 3 4 5 3 4 5 3
3 4 6 7 4 6 7 4
3 5 7 8 5 7 8 5
3 6 7 7 6 7 7 6
3 7 7 7 7 7 7 7
3 8 7 7 8 7 7 8
4 9 10 11 9 10 11 9
4 10 12 13 10 12 13 10
4 11 13 14 11 13 14 11
4 13 13 13 13 13 13 13
5 15 16 17 15 16 17 15
5 18 18 18 18 18 18 18
6 19 20 20 19 20 20 19
6 20 20 20 20 20 20 20
7 21 22 22 21 22 22 21
7 22 22 22 22 22 22 22
8 23 24 24 23 24 24 23
8 24 24 24 24 24 24 24
9 25 26 26 25 26 26 25

@COLORS

0 31 31 31
1 255 0 0
2 223 31 95
3 0 254 0
4 0 0 159
5 38 38 84
6 31 159 47

@ICONS

XPM
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"PJ c #003000"
"AK c #D41D5A"
"BK c #E01F5F"
"CK c #7E0000"
"DK c #13132A"
"EK c #007C00"
"FK c #000700"
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"KL c #1FA430"
"LL c #00BC00"
"ML c #004700"
"NL c #001E00"
"OL c #006A00"
"PL c #1F9E2F"
"AM c #650000"
"BM c #F90000"
"CM c #001800"
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"NM c #9A0000"
"OM c #00F900"
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"AN c #170000"
"BN c #000C00"
"CN c #13611D"
"DN c #003200"
"EN c #CF0000"
"FN c #0E0E20"
"GN c #062009"
"HN c #007E00"
"IN c #280000"
"JN c #24244F"
"KN c #720000"
"LN c #BC0000"
"MN c #5F0000"
"NN c #005500"
"ON c #4C0000"
"PN c #831238"
"AO c #00A100"
"BO c #070710"
"CO c #E51F61"
"DO c #1D1D41"
"EO c #88133A"
"FO c #00C400"
"GO c #00EA00"
"HO c #007500"
/* icon for state 1 */
"..........ECGJLNGKOJMK........"
"......INBMIKPKGCGCPKIKNC......"
"......MFPKPKIKAJLJIKGCIKKN...."
"....GAIKGCIKIL....HEPKGCME...."
"....IMPKGCEN......DFIKGCIKIL.."
"....KAGCGCNM......ALIKGCIKMN.."
"....IKGCGCKI........IKGCGCHF.."
"....IKGCGCAB........IKGCGCCK.."
"....IKGCGCGG........IKGCIKKH.."
"....DGGCGCGJ......ANIKGCIKPD.."
"....LEPKGCEL......HBIKGCIKID.."
"....PEIKGCIKAB..AHBEPKPKDG...."
"......BDPKPKIKIKIKPKPKIKNJ...."
"......OFJLIKIKGCIKIKIKJJ......"
"..........FBAMNKNGON.........."
/* icon for state 2 */
"............OENIBJIC.........."
"............FMOBPBIF.........."
"......HKPNLKBBPBPBIF.........."
"......IFPBPBPBPBPBIF.........."
"......EOIFGMAKPBPBIF.........."
"............GMPBPBIF.........."
"............IFPBPBIF.........."
"............IFPBPBIF.........."
"............IFPBPBIF.........."
"............IFPBPBIF.........."
"............IFPBPBIF.........."
"......LFMMLGFLPBPBFLLGMMLF...."
"......CGCOLIBKPBPBBKLICOCG...."
"......CGCOCOCOCOCOCOCOCOCG...."
"......FGEMMMMMMMMMMMMMMMLF...."
/* icon for state 3 */
"..........OLJELLLBHIDN........"
"......EGOMHMCJOCOCCJHMAO......"
"......AECJCJHMNEKKHMOCHMFA...."
"....JHHMOCHMPJ....HGCJOCHJ...."
"....BHCJOCEE......MBHMOCHMPJ.."
"....GFOCOCPG......BNHMOCHMFJ.."
"....HMOCOCPM........HMOCOCPF.."
"....HMOCOCMJ........HMOCOCHN.."
"....HMOCOCDJ........HMOCHMCL.."
"....HLOCOCJE......DCHMOCHMNN.."
"....KMCJOCGO......KJHMOCHMNL.."
"....JKHMOCHMMJ..CMMGCJCJHL...."
"......KCCJCJHMHMHMCJCJHMML...."
"......FKFOHMHMOCHMHMHMFE......"
"..........EHOIEKHODA.........."
/* icon for state 4 */
"..........CDCFKFJFGEEB........"
"......PAMHPHNHOHOHNHIIAF......"
"......LHNHNHDIIGGHOHOHBIGD...."
"....EDPHOHGICB....AGNHOHMH...."
"....NFNHOHJG......IBDIOHEICB.."
"....GHOHOHKE......EAIIOHBIMC.."
"....EIOHOHCE........JIOHOHJD.."
"....JIOHOHMD........JIOHOHLD.."
"....CIOHOHDE........JIOHOHGD.."
"....DHOHOHCF......HAIIOHBICC.."
"....FFNHOHFH......FCBIOHIIJA.."
"....ACCIOHBIOD..IAFHNHNHDH...."
"......OGNHNHBIJIGINHNHGIKB...."
"......BABGIIPHOHOHCIBIFC......"
"..........NAADLDHDNB.........."
/* icon for state 5 */
"............LMDKDKFN.........."
"............GLKDKDDO.........."
"......LACAEJKDKDKDDO.........."
"......DOKDKDKDKDKDDO.........."
"......JCDODOJNKDKDDO.........."
"............DOKDKDDO.........."
"............DOKDKDDO.........."
"............DOKDKDDO.........."
"............DOKDKDDO.........."
"............DOKDKDDO.........."
"............DOKDKDDO.........."
"......JMGBBOIEKDKDIEBOGBJM...."
"......JBKGKGKDKDKDKDKGKGJB...."
"......JBKGKGKGKGKGKGKGKGJB...."
"......DLBOGBGBGBGBGBGBGBJM...."
/* icon for state 6 */
"............PIDMHCIJ.........."
"............DDPLFIMA.........."
"......FDMIOKDBFIFIMA.........."
"......MAFIFIFIFIFIMA.........."
"......CNMAIHNDFIFIMA.........."
"............IHFIFIMA.........."
"............MAFIFIMA.........."
"............MAFIFIMA.........."
"............MAFIFIMA.........."
"............MAFIFIMA.........."
"............MAFIFIMA.........."
"......LCCHBFBCFIFIBCBFCHLC...."
"......PCOAKLDBFIFIDBKLOAPC...."
"......PCOAOAOAOAOAOAOAOAPC...."
"......HHGNCHCHCHCHCHCHCHLC...."
/* icon for state 7 */
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIAIAIAIAIAIAIAIAIAI"
"BLAIAIAIAIAIEFBLBLBLBLBLBLBLBL"

XPM
/* width height num_colors chars_per_pixel */
"7 49 160 2"
/* colors */
".. c #000000"
"BA c #940000"
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"IH c #115619"
"JH c #300614"
"KH c #187D25"
"LH c #FB0000"
"MH c #410000"
"NH c #004400"
"OH c #C20000"
"PH c #AF184B"
"AI c #00B600"
"BI c #004100"
"CI c #B4194C"
"DI c #008D00"
"EI c #0F5017"
"FI c #2C0000"
"GI c #00FF00"
"HI c #8E133C"
"II c #006100"
"JI c #060000"
"KI c #00FC00"
"LI c #20A530"
"MI c #001200"
"NI c #120208"
"OI c #15152D"
"PI c #13641D"
"AJ c #15152F"
"BJ c #8C133B"
"CJ c #610000"
"DJ c #005B00"
"EJ c #91143D"
"FJ c #003200"
"GJ c #00CD00"
"HJ c #00F300"
"IJ c #7E1136"
"JJ c #F30000"
"KJ c #000600"
"LJ c #002C00"
"MJ c #8F143D"
"NJ c #CD0000"
"OJ c #1D1D42"
"PJ c #DE1E5E"
/* icon for state 1 */
"..BGGAJANJIB.."
"..DCMFBCOFGC.."
"..MGDD..HAMGAH"
"..MGHH..NFMGMH"
"..MGEB..CJMGFI"
"..BBLHOCEGJJ.."
"..JIBAOHLFCH.."
/* icon for state 2 */
"......CING...."
"..FGPFPJIJ...."
"..NIJHJGIJ...."
"....DGKAIJ...."
"....MEKAKF...."
"..NBGGEAPHJF.."
"..MDEJHIMJBJ.."
/* icon for state 3 */
"..MICBJDGJIG.."
"..PGBDNHADKI.."
"..GIBE..DJGIFJ"
"..GIDI..HEGIBI"
"..GIFD..IIGILJ"
"..AICCJBIFHJ.."
"..KJLEEHHGNE.."
/* icon for state 4 */
"..FANDIEDEPA.."
"..PDJEGBDEAF.."
"..EFPC..LBFFOA"
"..HFJC..HBFFFB"
"..BFCD..OBGFNA"
"..LDOEACGEJE.."
"..CALCODEDIA.."
/* icon for state 5 */
"......NCCE...."
"..FCHCMAAJ...."
"..CFDBEEAJ...."
"....GDEEAJ...."
"....KBEEAJ...."
"..KCOIHCOJKG.."
"..OGIDHDIDMB.."
/* icon for state 6 */
"......PBPE...."
"..LGLAKDFE...."
"..AGMCECFE...."
"....ICLIFE...."
"....ABLIFH...."
"..DHIHKEKHEI.."
"..DAAECGBHPI.."
/* icon for state 7 */
"GHDFDFDFDFDFGH"
"GHDFDFDFDFDFGH"
"GHDFDFDFDFDFGH"
"GHDFDFDFDFDFGH"
"GHDFDFDFDFDFGH"
"GHDFDFDFDFDFGH"
"GHDFDFDFDFDFGH" 

The simple example with interaction is

Code: Select all

#CXRLE Pos=-9,-3
x = 18, y = 7, rule = AntBitS7:T20,20
CDA12.ADC6$CDA12.BEF!

Python script to reverse

Code: Select all

# Reverse the reversible (3x3 reduced to 7 states)
# By Alex V,
# based on script by Paul Nasca, 
# based on the invert script by  Andrew Trevorrow

from glife import rect
from time import time
import golly as g

r = rect( g.getrect() )
if r.empty: g.exit("The pattern is empty.")

oldsecs = time()
maxstate = g.numstates() - 1
swp = [0, 3, 6, 1, 4, 5, 2]

for row in xrange(r.top, r.top + r.height):
	for col in xrange(r.left, r.left + r.width):
		cell=g.getcell(col, row)
		cell = swp[cell]
		g.setcell(col, row, cell )

Alex V

[alexv]

Brian

I checked, idea of reversible extension with two kinds of ants and seven states I used earlier
may work with diagonal ants as well. Instead of single mark in rule definition above we may
use two different marks (conditions) and update rules:
No mark (condition 0): 1<->2, 4<->5
Mark #1 (condition 1): 0->1->3->2->0, 4<->5
Mark #2 (condition 2): 0->4->6->5->0, 1<->2

I see, two last exchanges for marks #1 and #2 are missed in your code and
it may be enough for reversibility to add few lines in WirelessAntWorld.java

Code: Select all

...
if (orthCond)
    { 
...
      else if (cell == 4)
        return 5;
      else if (cell == 5)
        return 4; 
}

...

if (diagCond)
    { 
...
      else if (cell == 1)
        return 2;
      else if (cell == 2)
        return 1; 
}
...

NOTE: To inverse evolution: 1<->2, 4<->5
(script in my previous comment uses other exchanges, because numeration of states is different)

Alex V

UPDATE:
Sorry, I missed, orthCond and diagCond in Brian's program also should be changed,
I did not guess how to do that with minimal modification and
so below is rewritten step function for WirelessAntWorld.java

Code: Select all

public int step(int row, int column)
  {
    int N  = squareCell.getNeighbor(row - 1, column    );
    int NE = squareCell.getNeighbor(row - 1, column + 1);
    int E  = squareCell.getNeighbor(row    , column + 1);
    int SE = squareCell.getNeighbor(row + 1, column + 1);
    int S  = squareCell.getNeighbor(row + 1, column    );
    int SW = squareCell.getNeighbor(row + 1, column - 1);
    int W  = squareCell.getNeighbor(row    , column - 1);
    int NW = squareCell.getNeighbor(row - 1, column - 1);

    int NN = squareCell.getNeighbor(row - 2, column    );
    int EE = squareCell.getNeighbor(row    , column + 2);
    int SS = squareCell.getNeighbor(row + 2, column    );
    int WW = squareCell.getNeighbor(row    , column - 2);
    
    int CellType[] = {0,1,0,1,2,0,2};

    int cell = squareCell.getNeighbor(row, column);

    int cCount = 0;
    if (CellType[N] == 1)   cCount++;
    if (CellType[E] == 1)   cCount++;
    if (CellType[S] == 1)   cCount++;
    if (CellType[W] == 1)   cCount++;
    
    int dCount = 0;
    if (CellType[NW] == 1)  dCount++;
    if (CellType[NE] == 1)  dCount++;
    if (CellType[SE] == 1)  dCount++;
    if (CellType[SW] == 1)  dCount++;
    
    int cdCount = 0;
    if (CellType[NW] == 2)  cdCount++;
    if (CellType[NE] == 2)  cdCount++;
    if (CellType[SE] == 2)  cdCount++;
    if (CellType[SW] == 2)   cdCount++;
    
    int ddCount = 0;
    if (CellType[NN] == 2)  ddCount++;
    if (CellType[EE] == 2)  ddCount++;
    if (CellType[SS] == 2)  ddCount++;
    if (CellType[WW] == 2) ddCount++;
    
    int Cond = 0;
    if ((ddCount == 0) && ((cdCount == 1) || (cdCount == 2)))
     Cond = 2;
    if ((dCount == 0) && ((cCount == 1) || (cCount == 2)))
     Cond = 1;       
    
    if ((Cond > 0) && (CellType[cell] != 0))
      Cond = CellType[cell];  
            
    if ((Cond == 1))
    {
      if (cell == 0)
        return 1;
      else if (cell == 1)
        return 3;
      else if (cell == 3)
        return 2;
      else if (cell == 2)
        return 0;
      else if (cell == 4)
        return 5;
      else if (cell == 5)
        return 4; 

    }
    
    if (Cond == 2)
    {
      if (cell == 0)
        return 4;
      else if (cell == 4)
        return 6;
      else if (cell == 6)
        return 5;
      else if (cell == 5)
        return 0;
      else if (cell == 1)
        return 2;
      else if (cell == 2)
        return 1; 
    }
    if (Cond == 0)
    {
      if (cell == 1)
        return 2;
      else if (cell == 2)
        return 1;
      else if (cell == 4)
        return 5;
      else if (cell == 5)
        return 4;
    }
    return cell;
  }

[bprentice]

Shura,

Thank you for the new version of step. I've implemented it in the 7 state program. I've also added a new control in both the 4 state and 7 state programs. This control reverses patterns with the V key.

The new versions can be downloaded here:

http://bprentice.webenet.net/Java%20Squ ... 0World.zip

Brian

[alexv]

The pattern with all possible input values for Fredkin gate

Code: Select all

#Fredkin Gate, loop with all possible combinations of input values
x = 165, y = 61, rule = WlAnt
34.2C72.2C$33.3C72.3C$33.2C74.2C4$67.2C6.2C$66.3C6.3C$57.2C7.2C8.2C7.
2C$56.3C26.3C$55.3C28.3C$55.2C30.2C$110.2C6.2C$61.2C18.2C26.3C6.3C$
60.3C18.3C25.2C8.2C$60.2C20.2C3$23.2C6.2C12.2C6.2C34.2C6.2C$.2C19.3C
6.3C10.3C6.3C32.3C6.3C50.2C$3C19.2C8.2C10.2C8.2C32.2C8.2C50.3C$2C149.
2C$19.BCA$27.2C20.2C20.2C20.2C19.2C$25.6C2.2C8.2C2.6C2.2C8.2C2.6C2.2C
8.2C2.6C2.2C8.13C6.2C$7.2C16.2C2.2C2.2C8.2C2.2C2.2C2.2C8.6C2.2C2.2C8.
2C2.2C2.2C2.2C8.5C2.6C6.3C25.2C$6.3C58.3C39.2C8.2C8.2C25.3C$6.2C59.2C
88.2C$19.BCA$38.2C42.2C20.2C8.2C8.2C$37.3C41.3C20.3C5.6C4.6C2.2C$13.
2C22.2C36.2C2.4C22.2C5.2C2.2C4.2C2.2C2.2C30.2C$12.3C60.6C24.2C55.3C$
12.2C63.2C84.2C$19.BCA$60.2C42.2C$59.4C40.3C$59.4C40.2C2$72.2C8.2C$9.
A28.2C32.3C6.3C25.2C$9.C28.3C30.4C6.4C23.3C$9.B29.2C30.2C10.2C23.2C3$
10.ACB47.ACB47.ACB$2C149.2C$3C147.3C$.2C147.2C3$47.ACB22.ACB$6.2C7.A
141.2C$6.3C6.C140.3C$7.2C6.B140.2C3$34.ACB72.ACB$12.2C149.2C$12.3C
147.3C$13.2C147.2C!

It is some "overclocking" because the gate formally needs 175 steps for operation,
but input values have only 25 steps delay.

PS: Yet another design for the same test (with "reflected loop")

Code: Select all

#Fredkin Gate, "reflected" loop with all combinations of input values
x = 180, y = 61, rule = WlAnt
49.2C72.2C$48.3C72.3C$48.2C74.2C4$82.2C6.2C$81.3C6.3C$72.2C7.2C8.2C7.
2C$71.3C26.3C$70.3C28.3C$70.2C30.2C$125.2C6.2C$76.2C18.2C26.3C6.3C$
75.3C18.3C25.2C8.2C$75.2C20.2C3$38.2C6.2C12.2C6.2C34.2C6.2C$13.2C22.
3C6.3C10.3C6.3C32.3C6.3C50.2C$12.3C22.2C8.2C10.2C8.2C32.2C8.2C50.3C$
12.2C152.2C2$42.2C20.2C20.2C20.2C19.2C$40.6C2.2C8.2C2.6C2.2C8.2C2.6C
2.2C8.2C2.6C2.2C8.13C6.2C$7.2C31.2C2.2C2.2C8.2C2.2C2.2C2.2C8.6C2.2C2.
2C8.2C2.2C2.2C2.2C8.5C2.6C6.3C25.2C$6.3C73.3C39.2C8.2C8.2C25.3C$6.2C
74.2C88.2C2$53.2C42.2C20.2C8.2C8.2C$52.3C41.3C20.3C5.6C4.6C2.2C$.2C
49.2C36.2C2.4C22.2C5.2C2.2C4.2C2.2C2.2C30.2C$3C87.6C24.2C55.3C$2C90.
2C84.2C2$75.2C42.2C$74.4C40.3C$74.4C40.2C2$87.2C8.2C$53.2C32.3C6.3C
25.2C$53.3C30.4C6.4C23.3C$54.2C30.2C10.2C23.2C3$15.ACB22.ACB22.ACB72.
ACB$2C176.2C$3C174.3C$.2C174.2C3$15.ACB22.ACB47.ACB22.ACB$6.2C164.2C$
6.3C162.3C$7.2C162.2C$164.B$164.C$15.ACB47.ACB47.ACB46.A$12.2C152.2C$
12.3C150.3C$13.2C150.2C!

[alexv]

Some standard circuits (additional "garbage" lines are due to reversibility)

Half adder

Code: Select all

# Half adder with three input examples
# First and second input line for bits
# First and second output lines for sum and carry
# Last output line for "garbage"
x = 120, y = 36, rule = WlAnt
89.2C14.2C$69.2C6.2C9.3C14.3C$68.3C6.3C8.2C16.2C$64.2C2.2C8.2C$63.3C$
63.2C42.2C$73.2C18.4C4.2C3.3C$73.2C18.4C4.2C3.2C$30.BCA27.BCA17.3C4.
2C5.2C$68.2C10.3C4.3C$67.3C3.2C13.2C$67.2C4.2C13.3C23.2C$67.3C3.2C13.
3C8.2C12.3C$68.2C17.5C.4C.3C12.2C$BCA57.BCA24.2C.2C.4C.2C$73.2C19.2C$
73.2C$63.2C46.2C$63.3C38.2C4.3C$64.2C2.2C8.2C24.2C4.2C$68.3C6.3C$69.
2C6.2C2$78.2C38.2C$78.3C36.3C$79.2C8.2C8.2C16.2C$89.3C6.3C$90.2C6.2C
6$99.2C$99.3C$100.2C!

Full adder with three half adders

Code: Select all

# Full adder composed from three half adders (with all input examples)
# First three input lines for bits and input carry
# First and second output lines for sum and output cary
# Last three lines for "garbage"
x = 354, y = 58, rule = WlAnt
184.2C7.4C6.4C6.4C17.2C58.2C7.4C6.4C6.4C17.2C$183.3C7.4C6.4C6.4C17.3C
56.3C7.4C6.4C6.4C17.3C$183.2C9.2C8.2C8.2C19.2C56.2C9.2C8.2C8.2C19.2C
2$263.2C14.2C$243.2C6.2C9.3C14.3C$242.3C6.3C8.2C16.2C$189.2C8.2C8.2C
8.2C17.2C2.2C8.2C45.2C8.2C8.2C8.2C$189.3C6.4C6.4C6.3C16.3C59.3C6.4C6.
4C6.3C$190.2C6.4C6.4C6.2C17.2C42.2C17.2C6.4C6.4C6.2C$213.2C14.2C16.2C
18.4C4.2C3.3C40.2C14.2C$193.2C6.2C9.3C14.3C15.2C18.4C4.2C3.2C21.2C6.
2C9.3C14.3C$BCA57.BCA57.BCA57.BCA9.3C6.3C8.2C16.2C22.3C4.2C5.2C32.3C
6.3C8.2C16.2C$188.2C2.2C8.2C38.2C10.3C4.3C34.2C2.2C8.2C$187.3C41.2C8.
3C3.2C13.2C33.3C41.2C$187.2C42.2C8.2C4.2C13.3C23.2C7.2C42.2C$197.2C
18.4C4.2C3.3C8.3C3.2C13.3C8.2C12.3C17.2C18.4C4.2C3.3C$197.2C18.4C4.2C
3.2C10.2C17.5C.4C.3C12.2C18.2C18.4C4.2C3.2C$30.BCA27.BCA87.BCA27.BCA
21.3C4.2C5.2C41.2C.2C.4C.2C40.3C4.2C5.2C$192.2C10.3C4.3C33.2C19.2C32.
2C10.3C4.3C$191.3C3.2C13.2C33.2C52.3C3.2C13.2C$191.2C4.2C13.3C22.2C
46.2C6.2C6.2C4.2C13.3C23.2C$191.3C3.2C13.3C8.2C12.3C38.2C4.3C5.3C6.3C
3.2C13.3C8.2C12.3C$192.2C17.5C.4C.3C13.2C2.2C8.2C24.2C4.2C6.2C8.2C17.
5C.4C.3C12.2C$90.BCA27.BCA27.BCA27.BCA28.2C.2C.4C.2C18.3C6.3C67.2C.2C
.4C.2C$197.2C19.2C23.2C6.2C54.2C19.2C$197.2C108.2C$187.2C46.2C15.2C
38.2C3.2C46.2C$187.3C38.2C4.3C15.3C36.3C3.3C38.2C4.3C$188.2C2.2C8.2C
24.2C4.2C17.2C8.2C8.2C16.2C5.2C2.2C8.2C24.2C4.2C$192.3C6.3C30.3C26.3C
6.3C27.3C6.3C$193.2C6.2C32.2C2.2C6.4C6.4C3.2C.4C.2C8.2C19.2C6.2C$238.
3C6.4C6.4C6.4C11.3C$202.2C34.2C8.2C8.2C8.2C13.2C27.2C38.2C$202.3C107.
3C36.3C$203.2C8.2C8.2C88.2C8.2C8.2C16.2C$213.3C6.3C98.3C6.3C$214.2C6.
2C100.2C6.2C$230.2C11.2C8.2C8.2C8.2C3.2C17.2C$230.3C9.4C6.4C6.4C6.3C
3.3C15.3C$231.2C9.4C6.4C6.4C6.2C5.2C15.2C3$223.2C$223.3C$224.2C4$273.
2C$273.3C$274.2C4$333.2C$333.3C$334.2C!

Yet another full adder

Code: Select all

# Full adder composed from "2.5" half adders (with all input examples)
# "2.5" are two half adders and half adder without carry
# First three input lines for bits and input carry
# First and second output lines for sum and output cary
# Last three lines for "garbage"
x = 326, y = 58, rule = WlAnt
184.2C7.4C6.4C6.4C17.2C$183.3C7.4C6.4C6.4C17.3C$183.2C9.2C8.2C8.2C19.
2C$294.2C6.4C6.4C7.2C$263.2C14.2C12.3C6.4C6.4C7.3C$243.2C6.2C9.3C14.
3C11.2C8.2C8.2C9.2C$242.3C6.3C8.2C16.2C$189.2C8.2C8.2C8.2C17.2C2.2C8.
2C$189.3C6.4C6.4C6.3C16.3C$190.2C6.4C6.4C6.2C17.2C42.2C15.2C8.2C8.2C$
213.2C14.2C16.2C18.4C4.2C3.3C15.3C6.4C6.3C$193.2C6.2C9.3C14.3C15.2C
18.4C4.2C3.2C17.2C6.4C6.2C$BCA57.BCA57.BCA57.BCA9.3C6.3C8.2C16.2C22.
3C4.2C5.2C32.2C14.2C$188.2C2.2C8.2C38.2C10.3C4.3C34.2C.3C14.3C$187.3C
41.2C8.3C3.2C13.2C33.3C.2C16.3C$187.2C42.2C8.2C4.2C13.3C23.2C7.2C21.
2C$197.2C18.4C4.2C3.3C8.3C3.2C13.3C8.2C12.3C29.3C$197.2C18.4C4.2C3.2C
10.2C17.5C.4C.3C12.2C30.2C$30.BCA27.BCA87.BCA27.BCA21.3C4.2C5.2C41.2C
.2C.4C.2C32.4C4.2C$192.2C10.3C4.3C33.2C19.2C36.4C4.2C$191.3C3.2C13.2C
33.2C58.2C$191.2C4.2C13.3C22.2C46.2C6.2C6.2C$191.3C3.2C13.3C8.2C12.3C
38.2C4.3C5.3C6.2C$192.2C17.5C.4C.3C13.2C2.2C8.2C24.2C4.2C6.2C8.2C$90.
BCA27.BCA27.BCA27.BCA28.2C.2C.4C.2C18.3C6.3C48.2C8.2C$197.2C19.2C23.
2C6.2C49.3C3.2C.3C$197.2C104.2C2.3C.2C$187.2C46.2C15.2C38.2C13.2C$
187.3C38.2C4.3C15.3C36.3C$188.2C2.2C8.2C24.2C4.2C17.2C8.2C8.2C16.2C
31.2C$192.3C6.3C30.3C26.3C6.3C42.2C4.3C$193.2C6.2C32.2C2.2C6.4C6.4C3.
2C.4C.2C8.2C33.2C4.2C$238.3C6.4C6.4C6.4C11.3C$202.2C34.2C8.2C8.2C8.2C
13.2C$202.3C$203.2C8.2C8.2C72.2C13.2C$213.3C6.3C72.3C11.3C$214.2C6.2C
74.2C11.2C$230.2C11.2C8.2C8.2C8.2C3.2C17.2C$230.3C9.4C6.4C6.4C6.3C3.
3C15.3C$231.2C9.4C6.4C6.4C6.2C5.2C15.2C3$223.2C$223.3C$224.2C4$273.2C
$273.3C$274.2C4$312.2C$312.3C$313.2C!

[alexv]

Adders from previous post use rather specific version of AND gate.
Alternative AND may be implemented also with so-called switch gate
(see "ANT" gate scheme from link below):
http://quantumbot.wordpress.com/2013/07 ... nto-logic/



Design may be still not optimal because produces more "garbage" in comparison
with previous one and each half adder uses two switch gates

Alternative half adder

Code: Select all

# Half adder with switch gates
# First and second input line for bits
# First and second output lines for sum and carry
x = 85, y = 31, rule = WlAnt
22.2C10.4C10.2C$21.3C10.4C10.3C10.2C16.2C$21.2C12.2C12.2C9.3C16.3C$
60.2C18.2C2$50.2C6.2C$18.4C27.3C6.3C13.2C$18.4C8.2C8.2C7.2C8.2C13.3C$
19.2C9.3C6.3C33.2C$BCA24.2C2.2C6.2C2.2C$26.3C14.3C8.2C19.2C$25.3C16.
3C5.6C2.2C8.2C3.3C$6.2C2.2C2.2C8.3C18.2C5.2C2.2C2.2C8.2C4.2C2.2C$6.6C
2.2C8.2C18.3C29.6C$8.2C34.2C32.2C$BCA28.4C4.2C$31.4C4.2C24.2C3.2C$3.
2C8.2C17.2C30.3C3.5C8.2C$3.3C6.3C11.2C36.2C5.5C6.3C$4.2C6.2C12.2C46.
2C6.2C$27.2C$27.2C8.2C$14.2C11.3C3.2C.3C$14.3C11.2C2.3C.2C$15.2C15.2C
2$49.2C$42.2C4.3C$22.2C13.2C3.2C4.2C$22.3C11.3C$23.2C11.2C!

Alternative 1-bit full adder

Code: Select all

# Full adder from half adders using switch gates
# First three input lines for bits and input carry
# First and second output lines for sum and output cary
x = 380, y = 37, rule = WlAnt
186.2C7.4C6.4C6.4C6.4C6.4C6.4C6.4C7.2C18.2C10.4C10.2C34.2C6.4C6.4C7.
2C$185.3C7.4C6.4C6.4C6.4C6.4C6.4C6.4C7.3C16.3C10.4C10.3C10.2C16.2C2.
3C6.4C6.4C7.3C$185.2C9.2C8.2C8.2C8.2C8.2C8.2C8.2C9.2C16.2C12.2C12.2C
9.3C16.3C.2C8.2C8.2C9.2C$324.2C18.2C2$191.2C8.2C8.2C8.2C8.2C8.2C8.2C
8.2C51.2C6.2C$191.3C6.6C4.4C2.8C6.4C6.4C6.4C6.3C19.4C27.3C6.3C13.2C
12.2C8.2C8.2C$192.2C6.6C4.4C2.8C6.4C6.5C5.4C6.3C19.4C8.2C8.2C7.2C8.2C
13.3C11.3C6.4C6.3C$203.2C12.2C12.2C9.3C16.3C19.2C9.3C6.3C33.2C12.2C6.
4C6.2C$BCA57.BCA57.BCA57.BCA59.2C18.2C27.2C2.2C6.2C2.2C47.2C14.2C$
190.2C98.3C14.3C8.2C19.2C11.2C.3C14.3C$189.3C40.2C6.2C21.2C24.3C16.3C
5.6C2.2C8.2C3.3C9.3C.2C16.3C$189.2C9.4C27.3C6.3C13.2C5.2C5.2C2.2C2.2C
8.3C18.2C5.2C2.2C2.2C8.2C4.2C2.2C5.2C21.2C$200.4C8.2C8.2C7.2C8.2C13.
3C11.6C2.2C8.2C18.3C29.6C27.3C$201.2C9.3C6.3C33.2C13.2C34.2C32.2C29.
2C$30.BCA27.BCA87.BCA27.BCA26.2C2.2C6.2C2.2C68.4C4.2C55.4C4.2C$208.3C
14.3C8.2C19.2C36.4C4.2C24.2C3.2C24.4C4.2C$207.3C16.3C5.6C2.2C8.2C3.3C
7.2C8.2C17.2C30.3C3.5C8.2C12.2C$188.2C2.2C2.2C8.3C18.2C5.2C2.2C2.2C8.
2C4.2C2.2C3.3C6.3C11.2C36.2C5.5C6.3C6.2C$188.6C2.2C8.2C18.3C29.6C4.2C
6.2C12.2C46.2C6.3C6.2C$190.2C34.2C32.2C29.2C53.2C8.2C$90.BCA27.BCA27.
BCA27.BCA30.4C4.2C68.2C8.2C53.2C8.2C$213.4C4.2C24.2C3.2C24.2C11.3C3.
2C.3C53.3C3.2C.3C$185.2C8.2C17.2C30.3C3.5C8.2C11.3C11.2C2.3C.2C55.2C
2.3C.2C$185.3C6.3C11.2C36.2C5.5C6.3C12.2C15.2C48.2C13.2C$186.2C6.2C
12.2C46.2C6.2C79.3C$209.2C102.2C30.2C31.2C$209.2C8.2C85.2C4.3C56.2C4.
3C$196.2C11.3C3.2C.3C65.2C13.2C3.2C4.2C57.2C4.2C$196.3C11.2C2.3C.2C
60.2C4.6C6.5C4.2C6.4C6.2C8.2C6.2C$197.2C15.2C63.3C5.5C6.4C4.3C6.4C6.
3C6.3C6.3C$279.2C8.2C8.2C5.2C8.2C8.2C6.2C8.2C$231.2C118.2C13.2C$224.
2C4.3C118.3C11.3C$204.2C13.2C3.2C4.2C41.2C9.2C8.2C15.2C8.2C16.2C10.3C
11.2C$204.3C11.3C52.3C7.4C6.4C13.4C6.4C14.4C8.3C$205.2C11.2C54.2C7.4C
6.4C13.4C6.4C14.4C8.2C!

[alexv]

There is some question relating terminology. The four-state second-order CA above may be derived from
irreversible two-states CA using rather simple construction. But I am not about the construction because
the question relevant with any two-states CA: Is there some special term for (two-state) CA with transition
rule defined only by three values: state of cell, sum of states of four side cells and sum of states of four
corner cells? Does some short notation exist (like B.../S... for life-like CA)?

[bprentice]

Is there some special term for (two-state) CA with transition
rule defined only by three values: state of cell, sum of states of four side cells and sum of states of four
corner cells?

Alexander,

George Maydwell, who is an inactive member of this forum, uses these ideas in his CA software here:

http://www.collidoscope.com/ca/welcome.html

There is a rule family implementation called "George Maydwell" in Square Cell here:

http://bprentice.webenet.net/Java%20Squ ... 20Cell.zip

You can learn about it by reading files GeorgeMaydwellRule.java, GeorgeMaydwellDialog.java and
GeorgeMaydwellOptionsDialog.java.

You can also view a demonstration here:

http://bprentice.webenet.net/Square%20C ... pplet.html

Adjust the window and cell sizes, click the New World button and select the George Maydwell rule, then set the world to random states and run the simulation.

Square Cell is designed to be expanded by adding new rule families. To add such a new rule family requires the coding of an extension to the rule class and of classes to display and obtain rule parameters and options. Would it be possible for you to add a reversible rule family?

Brian

[alexv]

Thank you, Brian.

Would it be possible for you to add a reversible rule family?

Yes, all rules above, except WlAnt-4, can be written in such a way. The step function
should be (I did not tested , but hope it's correct - UPDATED, no getCount necessary):

Code: Select all

public int step(int r, int c)
  {
    int adjacentCount =
      (squareCell.getNeighbor(r - 1, c    ) % 2) +
      (squareCell.getNeighbor(r + 1, c    ) % 2) +
      (squareCell.getNeighbor(r    , c - 1) % 2) +
      (squareCell.getNeighbor(r    , c + 1) % 2);
    int diagonalCount =
      (squareCell.getNeighbor(r - 1, c - 1) % 2) +
      (squareCell.getNeighbor(r - 1, c + 1) % 2) +
      (squareCell.getNeighbor(r + 1, c + 1) % 2) +
      (squareCell.getNeighbor(r + 1, c - 1) % 2);
    int cell = squareCell.getNeighbor(r, c);
    int cond = ruleTable[cell % 2][adjacentCount][diagonalCount];
   if (cond == 1)
    {
      if (cell == 0)
        return 1;
      else if (cell == 1)
        return 3;
      else if (cell == 3)
        return 2;
      else if (cell == 2)
        return 0;
    }
    else
    {
      if (cell == 1)
        return 2;
      else if (cell == 2)
        return 1;
    } 
  } 

The nonzero items for rule tables are
WlAnt:

Code: Select all

0 1 0
0 2 0
1 1 0
1 2 0

WlAnt-2

Code: Select all

0 1 0
0 2 0
0 3 0
0 4 0
1 1 0
1 2 0
1 3 0
1 4 0

WlAnt-3

Code: Select all

0 1 0
0 2 0
0 3 0
1 1 0
1 2 0
1 3 0

Alex

[bprentice]

Alexander,

Thank you for your quick response.

Yes, all rules above, except WlAnt-4, can be written in such a way.

Unless I am misunderstanding your code, this is not what I was hoping for. By family of rules I mean rules that share a common parameter structure and where all possible parameter values generate a rule which is a member of the family.

Look at the method setNewRule() in GeorgeMaydwellRule.java. This is the code that is executed when the N key is depressed. It generates a new member of the GeorgeMaydwell rule family using simplistic random techniques.

For interesting rules that are not members of a family, I usually make a new instance of Base Square Cell. Your 4 and 7 state rules included in

http://bprentice.webenet.net/Java%20Squ ... 0World.zip

are examples.

Brian

[alexv]

Brian

It is code for whole rule family described by ruleTable with 2 x 4 x 4 ( UPDATE: 2 x 5 x 5) items.
Three WlAnt rules between four
may be described by such a way and so may be considered as members of the family. WlAnt-4 may be
included by slight modification of step function and 2 x 5 x 4 ( UPDATE: 2 x 6 x 5) ruleTable.

Code: Select all

public int step(int row, int column)
  {
    int N  = squareCell.getNeighbor(row - 1, column    ) % 2;
    int NE = squareCell.getNeighbor(row - 1, column + 1) % 2;
    int E  = squareCell.getNeighbor(row    , column + 1) % 2;
    int SE = squareCell.getNeighbor(row + 1, column + 1) % 2;
    int S  = squareCell.getNeighbor(row + 1, column    ) % 2;
    int SW = squareCell.getNeighbor(row + 1, column - 1) % 2;
    int W  = squareCell.getNeighbor(row    , column - 1) % 2;
    int NW = squareCell.getNeighbor(row - 1, column - 1) % 2; 
    int adjacentCount = N + E + S + W;
    
    if ((adjacentCount == 2) && ( N == S))
     adjacentCount = 5;
       
    int diagonalCount = NE + NW + SE + SW;
    
    int cell = squareCell.getNeighbor(row, column);
    int cond = ruleTable[cell % 2][adjacentCount][diagonalCount];
    
    if (cond == 1)
    {
      if (cell == 0)
        return 1;
      else if (cell == 1)
        return 3;
      else if (cell == 3)
        return 2;
      else if (cell == 2)
        return 0;
    }
    else
    {
      if (cell == 1)
        return 2;
      else if (cell == 2)
        return 1;
    } 
  } 

But I found WlAnt-4 useful only on Penrose tilings and so for simplicity let's return to initial version.
My earlier tries with random generating some time ago produced almost no interesting results and
so I think that it is only reasonable to use dialogs with editing the rule table with possibility to
save and load it to file. Sorry I do not have experience with Swing and using Java only in about %0.1
of my software effort.

The interesting tables except three mentioned above are AntiAnts compliments,
http://ayvlasov.wordpress.com/2014/02/05/anti-ants/
e.g. AntiAnt-2 ( white color for empty cells and blue for state=3)

Code: Select all

0 0 4
0 1 4
0 2 4
0 3 4
1 0 4
1 1 4
1 2 4
1 3 4

The tables Ants and Anti-Ants may be joined together
http://ayvlasov.wordpress.com/2014/02/1 ... anti-ants/

Code: Select all

0 1 0
0 2 0
0 3 0
0 4 0
0 0 4
0 1 4
0 2 4
0 3 4
1 1 0
1 2 0
1 3 0
1 4 0
1 0 4
1 1 4
1 2 4
1 3 4

Alex

[bprentice]

Alexander,

The nonzero items for rule tables are
WlAnt:

Code: Select all

0 1 0
0 2 0
1 1 0
1 2 0

WlAnt-2

Code: Select all

0 1 0
0 2 0
0 3 0
0 4 0
1 1 0
1 2 0
1 3 0
1 4 0

WlAnt-3

Code: Select all

0 1 0
0 2 0
0 3 0
1 1 0
1 2 0
1 3 0

It is code for whole rule family described by ruleTable with 2 x 4 x 4 items.

I apologize for being slow, but I can't relate these two quotes. What are the complete rule tables and what is the range of values that they can contain?

I'm even more confused with the following two rule tables:

Code: Select all

0 0 4
0 1 4
0 2 4
0 3 4
1 0 4
1 1 4
1 2 4
1 3 4

Code: Select all

0 1 0
0 2 0
0 3 0
0 4 0
0 0 4
0 1 4
0 2 4
0 3 4
1 1 0
1 2 0
1 3 0
1 4 0
1 0 4
1 1 4
1 2 4
1 3 4

Brian

[alexv]

What are the complete rule tables and what is the range of values that they can contain?

Sorry if it was not clear. In the example with construction of four-state reversible CA from
two-state CA the rule table contains only 0 and 1. Line a b c in the list means that ruleTable[a,b,c] is unit.
All items not written in the list are zero. For all lists in examples rule table has dimensions 2x4x4 (UPD 2x5x5).

Alexander

PS. The format was developed 10 years ago, so please do not ask about reasons