Triangular neighborhood (Carter Bays' TriLife rules)

[EricG]

The following is hardly as nifty as gliders in Penrose tiling, but it might be of interest.

Chapter 17 of Andrew Adamatzky's "Game of Life Cellular Automata" is The Game of Life in Non-Square Environments, by Cater Bays. In the section of the chapter on triangular grids, Bays discusses the 12 neighbor triangular Moore neighborhood, and presents two rakes which work in rule B3/S278. Andrew from this forum created an icon scheme and an accompaying script which allows Golly users to try out different rules. The download from the ruletable repository didn't include RLEs for Bays' two rakes, so I used Andrews' script to create a B3/S278 ruletree and then manually entered the rake patterns, working off Bays' diagrams.

Here are Carter Bays' two rakes, as shown in Figure 17.10 of Adamtzky's book:

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x = 39, y = 12, rule = TriLife-B3S278
4.C$2.C2.C19.A$2.BC.A18.2BA$36.CA$36.B.A$37.AC5$BC$.A!

To create the ruletree for this rule, you can download Andrew's script and associated files here:
http://code.google.com/p/ruletablerepos ... ighborhood
Andrew's script works well, and the icon scheme is very clever. Thanks Andrew!
For new people: if you have any questions about how to set this up, please don't hesitate to ask.

Whether you are looking at the rakes, or just looking at random fields, be sure to zoom in close enough to see the triangular icons - the rule looks much more interesting that way.

I thought that would be it for this subject, but it turns out there is more.

First off, even though it was tricky to count the triangles and convert to squares for the above pattern, I thought it was worth doing because surely rakes in a triangular neighborhood are rather unusual. Nope! Or at least, not in this rule. In Trilife-B3S278, the "large ship" and the "small ship" are both quite common, and since the large ship is also quite sparky, it is very easy to construct rakes. I'm willing to bet Carter Bays was working with much simpler editors than Golly, and that made it harder to find rakes.

The most interesting rake in the rake collection below is the leftmost one -- it's a forward rake (my favorite kind!). The large ships leave behind a trail of the slower small ships traveling in the same direction. Usefully, the stream of small ships is off to one side, and that allows it to interact with nearby rake streams.

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x = 1382, y = 292, rule = TriLife-B3S278
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143.B127.2C29.CA255.B175.A.A$22.CB368.B114.CB57.A.B118.CBA27.BA23.A
76.CA48.A.B28.A432.B.A6.A$24.C367.C112.2C58.AC2.A27.BA88.A2.C27.B23.B
75.BC.B46.AC2.A27.B250.2A180.2CA6.CB$23.ABA479.B59.BC2A26.A91.B2.BC
25.B25.B74.2CBC13.2A10.A20.BC2A278.BABC180.BA8.C$23.2BA480.B2A57.B28.
2C91.BCBC.A126.BCB11.C2.A9.CA20.B206.A.A72.B2.C181.BA6.BA$595.A.B91.B
.C2.A44.2A81.A9.A.A2.BA9.B227.BA75.BA179.B9.AC$594.AC2.A94.BC22.B20.B
C.C79.B2A7.C3.C2.B497.A2.A4.B$594.BC2A93.A.C26.A17.BA.B89.BA2.AC502.B
$20.CBA543.CBA26.B115.2C5.A.B19.C83.ABA5.B.3B3A29.CBA467.C$20.A.B543.
BA.A141.ABA110.2BA11.B30.BA.A$20.B.A232.BCA309.B143.B2A5.C150.B$256.C
A310.A143.B103.CBA27.BA23.A274.CA$256.ABA309.B26.CBA121.BA95.A2.C27.B
23.B274.A$259.A309.B25.BA.A217.B2.BC25.B25.B273.B.B$257.A.CA335.B144.
CA74.BCBC.A324.BA$258.2B305.2A30.A145.A19.C54.B.C2.A44.2A$22.C480.B2A
58.BC.C29.B143.B.B19.B.B56.BC22.B20.BC.C198.A$23.B479.BAB58.BA.B30.B
144.C76.A.C26.A17.BA.B200.B$22.BCA479.C61.C273.2C5.A.B19.C203.C.A66.
2A$505.AC87.2A244.ABA227.BA3.B66.B.C$294.CA210.B86.BC.C13.CA228.B2A5.
C295.C$294.ABA132.A2.B160.BA.B13.A129.2A99.B$294.B2.BA130.A2.C162.C
14.B128.BAB106.BA$295.B3.A129.B.C308.BA$21.CBA28.CA376.BC135.CA301.CA
$21.B30.A516.A302.A19.C$52.B.B512.B.B300.B.B19.B.B243.C$53.BA514.C
302.C194.BA69.A$596.CA466.BCB2CA68.BA$598.A141.BA323.C2.B$596.B.B143.
A323.A.B$566.2A30.C143.C126.2A196.B$21.2C375.A166.BAB155.A144.BAB$22.
B377.A165.BA157.A143.BA$400.C105.B.A216.C408.A$506.A.B86.2A537.CA$
506.BAC85.BAB537.B234.A.A$595.BA144.A10.A616.B.A6.A$741.CA8.B2.A614.
2CA6.CB$566.BA174.B8.BA2.A113.BA499.BA8.C$22.CA544.A29.A153.CA3C114.A
189.CA309.BA6.BA$568.C31.BA154.C114.C189.ABA306.B9.AC$23.A86.A488.BC.
A249.A208.B2.BA64.C241.A2.A4.B$109.BC154.AC328.BA2.A2B252.A207.B3.A
63.B244.B$20.C89.B154.B.C329.A.B254.C277.B242.C$23.A243.BA17.C.A132.C
BA173.C3.2A137.BA54.A9.BA$266.B2A17.B134.A179.BA138.B53.C9.B.B222.CA$
21.AB244.B19.BAC131.BAB143.A172.B65.A.A61.A10.A148.C.A90.B$21.B545.CA
227.B73.CA8.B2.A145.C2.B89.A$20.BA546.B302.B8.BA2.A144.A2.B89.B2.A$
504.BCA285.C2A9.CB75.CA3C171.2A$505.A69.2A220.A8.C78.C170.BCB66.BA$
21.2A483.C67.BA.C157.B56.ACA.AB6.B.BA248.B2.C$20.B.BC551.A2.A155.B.AB
59.C7.CA.B2.A245.CA68.C$23.B552.3A.A151.B3AB.A57.BA8.B3.BC307.A$21.B.
C542.BA9.BC.A152.BC.A.A64.2C5.B58.BA247.BCA$22.BC543.B12.BA152.CA69.A
64.B247.B2.A$23.2C541.B12.BA155.A3.AB127.B249.A.B2A$580.CA153.BC61.C
322.A2C$581.B541.B$20.2BA6.B536.B8.B2A$23.A4.A540.A5.BA161.CA$22.2C4.
B2.A535.A.B8.BA158.2C124.B$20.AC556.BC283.B.AB247.CBA$31.BA535.C292.B
3AB.A246.A.C$732.A129.BC.A.A185.C.A60.B$33.C534.BA149.A12.2CB77.C50.C
A188.B63.A$507.A58.A151.A13.2BA.B78.A49.A3.AB183.BAC60.B$22.A254.A
134.2C91.BAC58.2C166.B2.A126.BC251.B$22.CB253.B135.BAC150.A.B166.BCA
75.AB$24.C253.BC131.A2.A150.AC2.A166.B76.B297.2A$23.ABA539.BC2A149.A
93.BA53.CA241.BABC$23.2BA386.B2.A150.B153.B146.2C242.B2.C$413.A.B302.
B.B392.BA$413.BAC397.2A$812.B.BC45.A187.A$20.CBA696.A95.B32.A12.2CB
184.2BA$20.A.B251.2C443.B2C91.B.C31.A13.2BA.B182.BAB$20.B.A253.A442.
2CBA.C.A87.BC47.B2.A$275.BA443.BAC.B.B88.2C47.BCA239.CA$721.C2.BA139.
B240.A$562.A284.A258.B.B$562.CB155.BA91.2BA34.B257.BA$506.A52.BCAB.B
155.CA93.A31.B.B$22.C483.2C52.A.ABCA154.B.A91.2C$23.B537.AC2.C.A154.B
67.A9.BA10.AC$22.BCA537.B2.2B4.A217.C9.B.B46.A253.2A$569.B.CA227.A.A
45.B2C251.B.C$568.B.A.A.A215.B57.2CBA.C.A188.A59.C$568.2BA4.A273.BAC.
B.B188.B$573.A.B210.C2A9.CB14.A35.C2.BA190.BC$575.C215.A8.C13.CB$21.C
BA245.A.A514.ACA.AB6.B.BA14.C31.BA$21.B247.BA520.C7.CA.B2.A9.ABA31.CA
$408.2B380.BA8.B3.BC9.2BA31.B.A246.C$409.2A386.2C5.B46.B246.A$799.A
298.BA2$505.B286.C19.CBA$575.2A235.A.B$505.BC67.BA.C234.B.A$575.A2.A
461.BC$576.3A.A460.BA51.A$577.BC.A513.CA$580.BA512.B$579.BA$580.CA
224.C7.C$581.B227.A5.B$575.B2A236.BCA$575.BA230.AB$283.A294.BA227.B
282.C$282.BCA293.BC226.BA282.B$1036.A.A53.B$1036.BA$719.A$260.BA245.B
A209.A364.B$257.BCB2CA244.A574.A$258.C2.B244.AB574.B2.A$259.A.B146.2B
$260.B148.2A94.B212.A366.BA$508.C211.B$718.B.B366.C$1079.A$1078.BCA$
719.A128.A180.A48.B2.A$130.BA587.B2C125.A183.B47.A.B2A$130.C2.A585.2C
BA.C.A306.C.A45.A2C$131.CABA429.CA154.BAC.B.B303.BA3.B47.B$20.2BA109.
2B430.A156.C2.BA$23.A540.B.C280.A$22.2C695.BA128.B$20.AC482.2C214.CA
125.B.B224.CBA$505.CA213.B.A351.A.C$505.C.A214.B353.B$505.A63.BA277.A
228.A$505.CA.A339.B2C226.B$506.2B63.C276.2CBA.C.A221.B$822.AB25.BAC.B
.B$250.2A570.B2.A24.C2.BA216.2A$249.BCB571.BAC244.BABC$249.B2.C595.BA
221.B2.C$250.CA597.CA222.BA$289.C118.2B439.B.A$291.A117.2A440.B$291.B
.A!

To be continued below.

[EricG]

Carter Bays calls his rakes "glider guns" (although he acknowledges that Life enthusiasts call them rakes, using their "fanciful jargon")

I wondered if other rules might make it easy to quickly find a stationary gun. It turns out the related rule B39/S278abc has a very very sparky spinning oscillator, and putting two of them together can create guns. Here are four very similar guns:

Code: Select all

x = 331, y = 66, rule = TriLife-B39S278abc
90.A$89.2BA$65.A23.BAB$64.BCA24.C3.2A$64.B2.A$65.A.B2A25.A228.C$67.A
2C26.B229.C$69.B$327.2C$326.C.BA$327.ACA$328.B2$225.2A$94.AB7.A121.B.
C86.BAC$70.2BA24.CA2.AB.B120.BAC86.C.A$17.BA51.A2.A21.A.2C2.CA212.CB$
14.BCB2CA75.BA6.2B222.C.A$15.C2.B2CBA47.2B23.C121.B109.A2.A$16.A.B.A
2.C49.A21.B2.A115.CAC2.A7.B.B87.CA10.AB$16.B3.B.2A72.BCBC.B.A110.A.B
11.A.B85.BAB9.B.C$100.2C.B110.BA2.BCA96.A$16.A3.A52.2BA25.B.C112.C2.B
C97.C$20.A53.B11.B129.BA$20.B2.CA60.C.C2A126.BA$19.BC3.A60.A.B.B127.C
2A2.BC$22.B.C2A58.B3.A133.B.A$21.2CA2.B50.CA139.BAC3.A.B$21.4B52.ABA
7.CAB135.A.A$24.CA51.B2.BA7.B$24.ABA51.B3.A$24.B2.A$25.BAB$27.B7$CA$A
$B$2.B.B.CA$5.BC2$208.A$207.B2C$207.BC$208.2C86.A7.A.2BC$209.2C4.CA
79.B7.B.CAB$210.B4.A.A79.BC8.B$215.B2C89.B$5.C208.BA82.A$5.C.A3.A2BA
202.C79.AB.A$5.B2.C2.BAB.A187.C10.2A.C.A77.BCBC9.2C$6.B7.A190.B10.AB.
C90.BC$6.A199.C9.C$6.CAB2.B192.AB$9.A2.B$10.A.BA193.BA89.BA$11.2B194.
AC90.AB$208.B90.C2A$302.AC$301.BC$302.B2A!

You can also use the oscillator to make a complete loop:

Code: Select all

x = 383, y = 272, rule = TriLife-B39S278abc
263.BA2.C$253.C2.BA5.BA3.C$253.A4.A5.2C$253.B$254.BAB$256.3BC10.BA$
127.A130.2B2CA7.BA$126.A.B131.B$126.B2.A3.2A3.C119.AB$127.BA3.BABC5.A
116.B2.A$133.BA.A.B123.A$135.A5.BA117.B.B$134.B2.ABACA119.BC$132.C5.B
CB$132.A5.B$132.BA.B3.2C60.2A$137.A2C61.2BC$138.B17.A22.A21.BA.B25.A
22.A$154.B24.B24.CA22.B24.B$152.ABA23.BC46.ABA23.BC$152.B4.C68.B4.C
43.A$277.A$277.C9$7.A3.BA68.A3.BA$B.B4.B.C24.CA45.B.C24.CA$C.AB7.A24.
A23.BC23.A24.A23.BC$13.B22.B22.C2.A24.B22.B22.C2.A$2.BA56.ACA71.ACA$
60.2B72.2B$C.A$.2C$2.B3$16.BC2B.C$15.C.A.BAB$15.C.B$17.CB.C$18.ABA
280.C$18.B282.C.A$302.2B20$326.A$326.A$326.B$19.CBA305.A22.C$19.A.B
305.C.B21.B2A$19.B.A305.BAC20.A2.B$350.CAC$350.BC3$354.A$355.B11.A$
355.CA10.2C$367.B.C2$366.BA$356.A$358.B7.AB.C$360.C.A4.A.A$357.BA3.B
10$20.2C$21.B$361.A$361.2C19$20.2A$19.B.BC$22.B$20.B.C$21.BC$22.2C
337.B.A$361.A.B$361.BAC19$19.CBA$19.A.B$19.B.A337.2C$360.CA$360.C.A$
360.A$360.CA.A$361.2B19$20.2C$21.B$361.A$361.2C10$20.A3.BA$13.B.B4.B.
C$13.C.AB7.A$26.B$15.BA2$13.C.A$14.2C10.BC$15.B11.A$28.B3$31.CA$30.CB
C$29.A2.B20.CBA305.B.A$29.2BA21.A.C305.A.B$32.C22.B305.BAC$56.A$56.B$
56.B20$79.2A$79.B.C282.A$81.C280.BAB$362.C.AC$365.A.C$361.ABA.B.C$
361.C.2ACA3$380.A$380.2C$380.B.C$247.2A72.2A$246.BCB71.BCB56.BA$246.B
2.C22.A22.A24.B2.C22.A22.A$247.CA23.B24.B23.CA23.B24.B7.AB.C$273.BC
24.C.A45.BC24.C.A4.A.A$296.BA3.B68.BA3.B9$105.C$105.B$107.B43.C4.A68.
C4.A$129.CA23.BAB46.CA23.BAB$129.A24.A22.BC24.A24.A$129.B22.B25.A.BA
21.B22.B17.A$179.C2A61.2CB$180.2B60.2C3.A.BA$244.A5.B$242.ACA5.C$120.
CA119.BCBAB2.A$120.A.A117.BA5.B$120.B123.A.B.BA$121.B2.A116.B5.CABA3.
BA$123.AB119.C3.2B3.B2.A$122.A131.A.B$111.BA7.B2C2A130.B$111.BA10.C3A
$126.ABA$129.A$117.2C5.B4.B$114.C3.BA5.BA2.C$115.C2.BA!

And you can do silly tricks like this:

Code: Select all

x = 268, y = 432, rule = TriLife-B39S278abc
31$30.C3.C$30.A3.A.A$30.B4.2C$31.B3.BA$34.2A$34.2B$80.A73.A73.A$54.A.
A23.CB24.CA20.A.A23.CB24.CA20.A.A23.CB$42.BCA11.C23.B.C23.C.A21.C23.B
.C23.C.A21.C23.B.C$43.CA60.C2.B70.C2.B$43.ABA59.A2.B70.A2.B$46.A$44.A
.CA$45.2B$42.CA$42.A$43.B$37.BCA$38.2C.A$41.BA2$222.A2.B$222.A2.C$
200.C21.B.C$200.B.B20.BC8$240.C3.C$240.A3.A.A$240.B4.2C$241.B3.BA$
244.2A$244.2B3$252.BCA$61.2A190.CA$60.BC.C189.ABA$60.BA.B192.A$62.C
191.A.CA$255.2B$252.CA$252.A$253.B$247.BCA$248.2C.A$251.BA16$62.BA$
64.A$64.C21$62.B$65.A$63.A.B2$64.C2$64.BA19$61.2A$60.BC.C$60.BA.B$62.
C23$62.BA$64.A$64.C21$62.B$65.A$63.A.B2$64.C2$64.BA19$61.2A$60.BC.C$
60.BA.B$62.C23$62.BA$64.A$64.C10$43.C3.C$43.A3.A.A$43.B4.2C$44.B3.BA$
47.2A$47.2B3$55.BCA$56.CA$56.ABA$59.A$57.A.CA$58.2B$55.CA$55.A35.2A$
56.B33.BC.B$50.BCA38.B$51.2C.A37.BAB$54.BA37.BC$93.BCA17$145.A$143.A
2.B$142.C2.BA$142.B4.C$117.CBA25.ABC$117.B2.A$119.AB8$147.A$146.C2.C
2.3BA$149.2B2.A2.B$121.ABC27.A5.A$121.C.B23.2C.A4.2B$121.B.CA$123.C2.
B7.BA15.B2A$124.2AB7.BA16.B$125.B2$137.2A$137.A2B$137.B2.C$138.C.BA$
129.C.A7.A.A$130.AC8.B$131.B!

So, despite (or because of) this rule having twice as many neighbors as hexagonal rules, the rule is very similar to Hexagonal Generations rules like Pinwheels and Nocturne. (See viewtopic.php?f=11&t=935#p6833)

Unfortunately, in gaining the spinning oscillator, we lose the large sparky ship from Trilife-B3S237, so rakes aren't easy in this rule. I looked at some related rules, but I didn't find a rule that supports the large sparky ship and the spinning oscillator. It might be fun to find an entirely different rule with different spaceships and oscillators which supports both rakes and guns.

[EricG]

I'm still working on how to edit patterns in these triangular CAs.

The ships in the two rules discussed above travel in six directions - the four orthogonal directions N,S,E, and W, and also two diagonal directions, NW and SE. (So, six directions, but not the same six directions you typically find in hexagonal neighborhood CAs.)

Code: Select all

Six directions:
x = 20, y = 17, rule = TriLife-B3S278
9.CA2$10.A$.CA2$3.A3$C16.A.A$B.B16.C5$9.B6.B2$9.BC6.BC!

To rotate patterns on the triangular grid, it is helpful to be able to swap state-1 cells with state-2 cells. Andrew posted a script which changes all selected cells of a particular state into another chosen state (eg all of state1 into state2). A very simple modification of this script will work for swapping states.

Save this script as swap-states.py:

Code: Select all

# swap-states.py 
# This is a modification of change-state.py 
# See note below.

# Change all cells from one given state to another given state.
# Works in any rule with more than 2 states.
# Author: Andrew Trevorrow (andrew@trevorrow.com), Oct 2009.

#  This version is modified so that the program swaps 
#  a given state with another given state. 
#  (Example: all selected state1 cells become state2 and also all 
#  selected state2s become state1).   
#  The trivial coding modification was marked with "Goldstein patch" 
#  and messages to the user were modified as well.

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

r = rect( g.getselrect() )
if r.empty: g.exit("There is no selection.")

maxstate = g.numstates() - 1
if maxstate == 1: g.exit("The current rule only has 2 states.")

result = g.getstring(
"Swaps all the cells in one state (the 1st number)\n" +
"with a different state (the 2nd number) where both\n" +
"numbers must be from 0 to " + str(maxstate) + ":",
"1 2", "Change state")

try:
   s1, s2 = result.split()
except:
   g.exit("Enter 2 numbers separated by a space.")
try:
   fromstate = int(s1)
except:
   g.exit("1st state is not a number: " + s1)
try:
   tostate = int(s2)
except:
   g.exit("2nd state is not a number: " + s2)
if fromstate < 0 or fromstate > maxstate:
   g.exit("1st state is out of range: " + s1)
if tostate < 0 or tostate > maxstate:
   g.exit("2nd state is out of range: " + s2)
if fromstate == tostate:
   g.exit("The given states are the same.")

changed = 0
total = float(r.wd) * float(r.ht)
oldsecs = time()
for row in xrange(r.top, r.top + r.height):
   # might be large pattern so show percentage done each second
   newsecs = time()
   if newsecs - oldsecs >= 1.0:
      oldsecs = newsecs
      g.show("Changing cell states: " +
             str(int(100 * (row - r.top) * r.wd / total)) + "%")
      g.update()

   # allow keyboard interaction
   g.dokey( g.getkey() )

   for col in xrange(r.left, r.left + r.width):
      if g.getcell(col, row) == fromstate:
         g.setcell(col, row, tostate)
         changed += 1
                          # Goldstein patch begins
      elif g.getcell(col, row) == tostate:
         g.setcell(col, row, fromstate)
         changed += 1
                          # Goldstein patch ends
if changed == 0:
   # better to beep in this case
   g.exit("There are no cells in state %d." % fromstate)
else:
   g.show("%d cells were swapped from state %d to state %d or vice versa."
          % (changed, fromstate, tostate))

Here's what I've been doing manually. I"m putting it in a code box to preserve the indentations.

Code: Select all

To rotate a ship:
  Select the ship's pattern and then,

    For ships facing North,

       To rotate the ship so that it is facing East,      
       use Golly's Rotate Clockwise editing command 
       and then use Golly's Flip Top-Bottom command.

       To rotate the ship so that it is facing West,
       use  Golly's Rotate Anticlockwise, 
       and then use Golly's Flip Top-Bottom, 
       and then run the swap-states.py script.

       To rotate the ship so that it is facing South,
       use Golly's Rotate Clockwise (or Anticlockwise) twice, 
       and then run the swap-states.py script.
   
       To rotate the ship so that it faces NorthWest, I'm not sure.

    For ships facing Northwest,
       
        To rotate the ship so that it is facing Southeast,
        use Golly's Rotate Clockwise (or Anticlockwise) twice, 
        and then run the swap-states script.

        To rotate the ship so that it faces N,S,E, or W, I'm not sure.

Rotating the ship from Northwest to North or West is tricky, and it is hard for me to see what to do. Here's the situation:

Code: Select all

x = 16, y = 19, rule = TriLife-B39S278abc
3.CA9.CA2$5.A9.A6$C$B$2.B7$C$B.B!

Any ideas?

[EricG]

There is a replicator in B38/S23. In B37/S23, the replicator gets more shiplike, but remains a replicator. Many B3 rules show the beginnings of this replicator. The replicator fails in these rules but it causes patterns to slowly explode (eg B3a/S23).

In B39/S23, the proto-replicator becomes a very sparky failed-replicator ship. You can find the sparky ship by drawing any random doodle. Pairs of the ship can make puffers, dirty rakes, and breeders, and they eventually occur naturally since the rule is explosive and generates many many copies of the sparky ship, Adding various combinations of Ba, Bb, Bc, Sa, Sb, and Sc to the rule allows the ship to exist, although in Trilfe-B39aS23, the ship turns into a puffer. If I'm not mistaken, some combinations make the rule a bit less explosive (eg B39bc/S23a, say, might be less explosive than others). It would be nice to find a non-explosive variant of the rule which includes the sparky ship.

Edit -- here's a clean rake in one of the variant rules:

Code: Select all

x = 118, y = 183, rule = TriLife-B39bS23
A11.BC$CA10.3B$BC11.2B$.CA$.BC$2.B2$16.2A$16.3A$17.CA2$3.BA2.C$3.BA3.
C$17.BA2.C$17.BA3.C3$7.C.BA4$5.CA8.CA$5.BCA.C3BA.2C$6.B.A2BACB.ABA$8.
B2.2B2.B2.C2A9.ACA$18.2BC2.B3.B2.BCB$22.B.B2.B.B$23.A6.A$25.A3.A4$25.
A$25.2C2A$25.3BC$28.B$27.A.ABA$26.C3.ACA$25.CBA$25.B2C3.BA$26.B4.A$
29.BAB9$32.BA$31.A.B$35.A2$35.C.B6$37.A$36.A.BA.A$36.B2.C.C$39.2BA$
37.B4CBA$40.BCACA$42.B$42.CA$42.BCA3$45.A$44.B2.A.A$47.BC2.A$49.A.A$
46.BA3.C$47.B3.BA$47.B$49.C13.B$63.CBA$63.BAC3$65.CBA$65.BAC$48.C18.A
$48.C18.B$48.B4.A13.CBA$53.C13.BAC$53.C2$42.C26.CBA$42.C26.BAC$42.B4.
A23.A$47.C21.BA2.C$47.C5.2A14.BA3.C$53.2B$36.C$36.C22.C$36.B4.A11.C6.
C$41.C12.C$41.C5.2A$47.2B8.B2.A$56.B3.B7.2B2$57.B13.C2A7.A$58.AB12.B.
C5.BA$57.2B2A$57.B$57.B2.B$57.B7.C$58.CAB5.C$57.B2.A$56.B2.B$57.A2.A$
59.C18.A$78.AB$79.2A5$71.C$72.C4$84.A$84.AB$85.2A5$77.C$78.C4$90.A$
90.AB$91.2A5$83.C$84.C2$77.A$76.C2BA$96.A$96.AB3.3B$77.B2.B16.2A2.B2A
C$78.A2.A20.C.BA$103.2B$104.2A$79.B2.B20.BA.C$79.B3.B5.C14.C2BA$79.B
4.B5.C14.3A$80.A.2A.A20.B$105.2CBCA$105.BA2.C$81.B.2B.B15.A$82.A4.A
14.AB$83.2A.2A15.2A2.C2.BA$107.BCA2C$109.A.A$84.C3.BA$83.B2.2B2.B$83.
C3.2A2.BA2.C13.A4.A$96.C12.ACA.C2A$84.A.B3.B2.A14.B.BC.BC.B$85.B6.B
16.2C4.BCA$109.BC5.BC$108.A$108.AB$109.2A5$98.C.BA!