FireWorld+

For discussion of other cellular automata.
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Yoel
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FireWorld+

Post by Yoel » May 16th, 2022, 10:50 am

UPDATE:

Read below the redefinition of the rule. The old one in now renamed FireWorld+old.


This is a somewhat baroque experimental 7-state rule, a superset of FireWorld that enables the following by adding 3 additional states:

1. Diagonal photons (diaphotons), which turn into electrons when they touch wires. The fading diaphoton state is distinct from the fading photon/electron state.

The wiring rules are the same as with the red (photonic) cells: a red cell is born, if surrounded by 1 green (diaphotonic) cell and 2 or 3 wire cells or by 1 orthogonal and 1 diagonal neighboring green cell and 2 or 3 wire cells. This enables trivial conversion of diaphotons into electrons, photons and photon splitters.

2. When two diaphotons touch each other in the orthogonal position, they turn into red cells, thus producing a photon and serving as a natural AND gate.

3. Crossings of photon and diaphoton streams enable natural p6 crossovers and p3 AND-NOT gates.

4. The white cells (state 6) serve as photon to diaphoton converters, diaphoton reflectors and splitters, OR gates and diodes.

As a superset of FireWorld (and the historical "small w" Fireworld), this rule is Turing complete.

The ruletable:

Code: Select all

@RULE FireWorld+

# A fancy combination of FireWorld rule with the Diaphotons rule

# FireWorld is the next generation of Fireworld (03ajkr/2ak/3), proven to be
# capable in itself of universal computation and suitable for constructing logic circuits.

# This new generation of Fireworld is a hybrid rule combining 03ajkr7/2ak/3 and
# a Wireworld-like wiring system. It is fully backward compatible with Fireworld.

# Wires are implemented as the fourth, immutable state. The new rules are as follows:

# 1. A cell is born, if surrounded by 1 living (state 1) cell and 2 or 3 wire cells (state 3).
# 2. A cell is born, if surrounded by 1 orthogonal and 1 diagonal neighboring living cell and 2 or 3 wire cells.

# The last rule mirrors the "2ak" behavior of Fireworld and helps to ignite electrons on wires by free photons.

# Diaphotons is a simple rule that allows spaceships to travel diagonally at the maximum "speed of light".

# The resulting combination rule allows to convert diaphotons to photons and electrons and vice versa.
# Diaphotons have their own 2 states. Another extra state converts photons to diaphtons.
# It also enables a diagonal diode and the OR gate. Interaction between diophotons enables the AND gate.

# As long as these extra states are not used, the rule is 100% backward compatible with FireWorld.

# Partially inspired by Brian Prentice's rule Mites

# Copyright by Yoel Matveyev, 2022
# The GNU General Public License v3.0

@COLORS

0 0 0 0
1 255 0 0
2 255 255 0
3 0 0 255
4 0 255 0
5 0 255 255
6 255 255 255

@TABLE

n_states:7
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1,2,3,4,5,6}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a

var i={0,2,5}
var j=i
var k=i
var l=i
var m=i
var n=i
var o=i
var p=i

# The original Fireworld augmented with S7

0,1,1,i,j,k,l,m,n,1
0,1,i,j,1,k,l,m,n,1
1,i,j,k,l,m,n,o,p,1
1,1,1,1,i,j,k,l,m,1
1,1,i,1,1,j,k,l,m,1
1,1,1,i,j,1,k,l,m,1
1,1,i,1,j,k,1,l,m,1
1,1,i,1,j,k,l,m,1,1
1,1,1,1,1,1,1,1,i,1
1,1,1,1,1,1,1,i,1,1


var a2={0,2,6}
var b2=a2
var c2=a2
var d2=a2
var e2=a2
var f2=a2
var g2=a2
var h2=a2

# Diaphtons

0,a2,4,c2,d2,e2,f2,g2,h2,4
0,4,b2,c2,d2,e2,f2,g2,h2,5
0,4,5,c2,d2,e2,f2,g2,h2,5

# A computer-generated list of all possible living cells and wire cells positions

0,i,j,1,l,m,3,o,3,1
0,i,j,3,3,m,n,1,p,1
0,i,j,3,l,1,n,3,p,1
0,i,j,3,l,1,n,o,3,1
0,i,j,3,l,3,n,1,p,1
0,i,j,3,l,3,n,o,1,1
0,i,j,3,l,m,3,o,1,1
0,i,j,3,l,m,n,1,3,1
0,i,j,3,l,m,n,3,1,1
0,i,j,k,3,3,n,o,1,1
0,i,j,k,3,m,1,o,3,1
0,i,j,k,3,m,3,o,1,1
0,i,j,k,3,m,n,1,3,1
0,i,j,k,3,m,n,3,1,1
0,i,j,k,l,1,3,o,3,1
0,i,j,k,l,1,n,3,3,1
0,i,j,k,l,3,1,3,p,1
0,i,j,k,l,3,1,o,3,1
0,i,j,k,l,3,3,1,p,1
0,i,j,k,l,3,3,o,1,1
0,i,j,k,l,3,n,1,3,1
0,i,j,k,l,3,n,3,1,1
0,i,j,k,l,m,3,1,3,1
0,i,j,k,l,m,3,3,1,1

0,3,j,3,l,3,n,1,p,1
0,i,3,k,3,m,3,o,1,1
0,i,j,1,3,m,3,o,3,1
0,i,j,1,l,3,3,o,3,1
0,i,j,1,l,3,n,3,3,1
0,i,j,1,l,m,3,3,3,1
0,i,j,3,1,3,n,o,3,1
0,i,j,3,1,m,3,o,3,1
0,i,j,3,3,1,n,o,3,1
0,i,j,3,3,3,n,1,p,1
0,i,j,3,3,3,n,o,1,1
0,i,j,3,3,m,1,3,p,1
0,i,j,3,3,m,1,o,3,1
0,i,j,3,3,m,3,1,p,1
0,i,j,3,3,m,3,o,1,1
0,i,j,3,3,m,n,1,3,1
0,i,j,3,3,m,n,3,1,1
0,i,j,3,l,1,3,3,p,1
0,i,j,3,l,1,3,o,3,1
0,i,j,3,l,1,n,3,3,1
0,i,j,3,l,3,1,3,p,1
0,i,j,3,l,3,1,o,3,1
0,i,j,3,l,3,3,1,p,1
0,i,j,3,l,3,3,o,1,1
0,i,j,3,l,3,n,1,3,1
0,i,j,3,l,3,n,3,1,1
0,i,j,3,l,m,3,1,3,1
0,i,j,3,l,m,3,3,1,1
0,i,j,k,3,3,3,o,1,1
0,i,j,k,3,3,n,1,3,1
0,i,j,k,3,3,n,3,1,1
0,i,j,k,3,m,1,3,3,1
0,i,j,k,3,m,3,1,3,1
0,i,j,k,3,m,3,3,1,1
0,i,j,k,l,1,3,3,3,1
0,i,j,k,l,3,1,3,3,1
0,i,j,k,l,3,3,1,3,1
0,i,j,k,l,3,3,3,1,1

0,i,j,1,3,m,1,o,3,1
0,i,j,1,3,m,3,o,1,1
0,i,j,1,l,3,n,3,1,1
0,i,j,1,l,3,1,o,3,1
0,i,j,1,l,3,3,o,1,1
0,i,j,1,l,m,3,3,1,1
0,i,j,1,1,m,3,o,3,1
0,i,j,3,l,1,3,o,1,1
0,i,j,3,l,1,n,3,1,1
0,i,j,3,l,1,1,o,3,1
0,i,j,3,l,3,n,1,1,1
0,i,j,3,l,3,1,1,p,1
0,i,j,3,l,m,3,1,1,1
0,i,j,3,1,3,n,1,p,1
0,i,j,3,1,m,3,1,p,1
0,i,j,3,1,m,n,1,3,1
0,i,j,3,1,1,n,3,p,1
0,i,j,3,1,1,n,o,3,1
0,i,j,3,3,m,1,1,p,1
0,i,j,3,3,m,n,1,1,1
0,i,j,3,3,1,n,o,1,1
0,i,j,k,3,m,3,1,1,1
0,i,j,k,3,1,3,o,1,1
0,i,j,k,3,1,n,3,1,1
0,i,j,k,3,1,1,o,3,1
0,i,j,k,3,3,n,1,1,1
0,i,j,k,l,1,3,3,1,1
0,i,j,k,l,1,1,3,3,1
0,i,j,k,l,3,1,1,3,1
0,i,j,k,l,3,3,1,1,1

0,3,1,3,l,3,n,1,p,1
0,3,1,1,l,3,n,3,p,1
0,i,3,1,3,m,3,o,1,1
0,i,3,1,l,3,n,3,1,1
0,i,3,1,l,3,1,o,3,1
0,i,3,1,1,m,3,o,3,1
0,i,3,3,l,1,3,o,1,1
0,i,3,3,l,1,n,3,1,1
0,i,3,3,l,1,1,o,3,1
0,i,3,3,l,3,n,1,1,1
0,i,j,1,3,m,1,3,3,1
0,i,j,1,3,m,3,3,1,1
0,i,j,1,3,3,n,3,1,1
0,i,j,1,3,3,1,o,3,1
0,i,j,1,3,3,3,o,1,1
0,i,j,1,l,3,1,3,3,1
0,i,j,1,l,3,3,3,1,1
0,i,j,1,1,3,n,3,3,1
0,i,j,1,1,3,3,o,3,1
0,i,j,1,1,m,3,3,3,1
0,i,j,3,l,1,3,3,1,1
0,i,j,3,l,1,1,3,3,1
0,i,j,3,l,3,1,1,3,1
0,i,j,3,l,3,3,1,1,1
0,i,j,3,1,3,n,1,3,1
0,i,j,3,1,3,3,1,p,1
0,i,j,3,1,m,3,1,3,1
0,i,j,3,1,1,3,o,3,1
0,i,j,3,1,1,n,3,3,1
0,i,j,3,3,m,1,1,3,1
0,i,j,3,3,m,3,1,1,1
0,i,j,3,3,1,3,o,1,1
0,i,j,3,3,1,n,3,1,1
0,i,j,3,3,1,1,3,p,1
0,i,j,3,3,1,1,o,3,1
0,i,j,3,3,3,n,1,1,1
0,i,j,3,3,3,1,1,p,1
0,i,j,k,3,1,3,3,1,1
0,i,j,k,3,3,1,1,3,1
0,i,j,k,3,3,3,1,1,1

# When touching a wire, a diagonal photons becomes an electron

0,i,j,4,l,m,3,o,3,1
0,i,j,3,3,m,n,4,p,1
0,i,j,3,l,4,n,3,p,1
0,i,j,3,l,4,n,o,3,1
0,i,j,3,l,3,n,4,p,1
0,i,j,3,l,3,n,o,4,1
0,i,j,3,l,m,3,o,4,1
0,i,j,3,l,m,n,4,3,1
0,i,j,3,l,m,n,3,4,1
0,i,j,k,3,3,n,o,4,1
0,i,j,k,3,m,4,o,3,1
0,i,j,k,3,m,3,o,4,1
0,i,j,k,3,m,n,4,3,1
0,i,j,k,3,m,n,3,4,1
0,i,j,k,l,4,3,o,3,1
0,i,j,k,l,4,n,3,3,1
0,i,j,k,l,3,4,3,p,1
0,i,j,k,l,3,4,o,3,1
0,i,j,k,l,3,3,4,p,1
0,i,j,k,l,3,3,o,4,1
0,i,j,k,l,3,n,4,3,1
0,i,j,k,l,3,n,3,4,1
0,i,j,k,l,m,3,4,3,1
0,i,j,k,l,m,3,3,4,1

0,3,j,3,l,3,n,4,p,1
0,i,3,k,3,m,3,o,4,1
0,i,j,4,3,m,3,o,3,1
0,i,j,4,l,3,3,o,3,1
0,i,j,4,l,3,n,3,3,1
0,i,j,4,l,m,3,3,3,1
0,i,j,3,4,3,n,o,3,1
0,i,j,3,4,m,3,o,3,1
0,i,j,3,3,4,n,o,3,1
0,i,j,3,3,3,n,4,p,1
0,i,j,3,3,3,n,o,4,1
0,i,j,3,3,m,4,3,p,1
0,i,j,3,3,m,4,o,3,1
0,i,j,3,3,m,3,4,p,1
0,i,j,3,3,m,3,o,4,1
0,i,j,3,3,m,n,4,3,1
0,i,j,3,3,m,n,3,4,1
0,i,j,3,l,4,3,3,p,1
0,i,j,3,l,4,3,o,3,1
0,i,j,3,l,4,n,3,3,1
0,i,j,3,l,3,4,3,p,1
0,i,j,3,l,3,4,o,3,1
0,i,j,3,l,3,3,4,p,1
0,i,j,3,l,3,3,o,4,1
0,i,j,3,l,3,n,4,3,1
0,i,j,3,l,3,n,3,4,1
0,i,j,3,l,m,3,4,3,1
0,i,j,3,l,m,3,3,4,1
0,i,j,k,3,3,3,o,4,1
0,i,j,k,3,3,n,4,3,1
0,i,j,k,3,3,n,3,4,1
0,i,j,k,3,m,4,3,3,1
0,i,j,k,3,m,3,4,3,1
0,i,j,k,3,m,3,3,4,1
0,i,j,k,l,4,3,3,3,1
0,i,j,k,l,3,4,3,3,1
0,i,j,k,l,3,3,4,3,1
0,i,j,k,l,3,3,3,4,1

# A red cell becomes green upon touching a trigger cell

0,6,1,k,l,m,n,o,p,4
0,1,6,k,l,m,n,o,p,4
0,6,j,1,l,m,n,o,p,4
0,i,1,k,6,m,n,o,p,4
0,1,j,k,6,m,n,o,p,4
0,6,j,k,1,m,n,o,p,4
0,6,j,k,l,1,n,o,p,4
0,i,6,k,l,m,1,o,p,4

# Two orthogonally ajacent green cells become red, enacling an AND gate

0,4,4,k,l,m,n,o,p,1
4,4,j,k,l,m,n,o,p,2
0,i,4,k,l,m,5,o,p,4

# Two green cells react with two white cells, enabling an OR gate

0,6,b2,c2,d2,6,4,g2,4,4
0,4,6,k,6,4,n,o,p,5

# Enabling a diagonal diode

0,6,6,3,l,m,n,o,4,4
0,3,4,k,l,m,n,o,p,4

# Cleaning up, making sure the wires are immutable

1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,0
3,a,b,c,d,e,f,g,h,3
4,a,b,c,d,e,f,g,h,0
5,a,b,c,d,e,f,g,h,0
6,a,b,c,d,e,f,g,h,6
When no wires, white or green cells are used, the rule is identical to my old historical Fireworld augmented with s7 (this detail almost never affects any pattern, including the Izhora computer, but turns blocks into p3 guns). The variety of Diaphotons in this rule is capable of producing red cells and acts somewhat similarly to my other experimental rule HyperBrain. However, only green cells can produce the red ones, not the other way around.

Code: Select all

x = 20, y = 25, rule = FireWorld+old
3$8.A2$10.DE2.A4$6.A2.ED3$6.A2.ED4$10.DE2.A2$8.A!

Code: Select all

x = 17, y = 25, rule = FireWorld+old
$5.DE$4.D$3.D7.DE$3.E3.ED$6.E.E$6.DED3$5.D$5.E2$6.E$6.D3$7.DED$7.E2.D
$4.E5.E$4.D4.ED$5.D7.DE$6.D$7.DE!

Code: Select all

x = 17, y = 24, rule = FireWorld+old
$7.DE$6.D$5.D7.DE$4.D4.ED$4.E5.E$7.E2.D$7.DED2$14.E$6.D7.D$6.E5.ED$6.
E5.ED$6.D7.D$14.E2$7.DED$7.E2.D$4.E5.E$4.D4.ED$5.D7.DE$6.D$7.DE!

Code: Select all

x = 23, y = 20, rule = FireWorld+old
2$8.DE$8.E2$8.E6.E.E$8.DE2.DE3.D$8.DE6.E$8.E2$16.D2.E$12.DED4.D$12.E.
E3.D$12.DE3.E$9.ED6.D$16.D$14.ED!

Code: Select all

x = 30, y = 31, rule = FireWorld+old
2$24.ED$26.D$18.ED7.D$19.EDE2.D2.E$18.EDE2$20.E3.E$20.DE.ED$25.ED$14.
ED10.E$15.2E$14.E2DE3$13.2B$13.2A3$11.2B$10.A.A$5.AB.B.A$5.AB.B!
Junctions, all beaming from the same p3 gun:

Code: Select all

x = 258, y = 135, rule = FireWorld+old
15$102.F11.F2$104.DE5.ED$104.E7.E2$107.DED$107.E.2F2$110.DE$110.E2$
113.DE$113.E$117.F$116.DF$116.E$116.DF$117.F.DE$113.E5.E$101.FE10.DE$
101.E20.DE$110.E11.E$104.DE4.DE$104.E2.F17.DE$107.F.2F14.E28.F$107.DE
D83.C$128.DE26.DE$104.E7.E15.E27.E38.DE$104.DE5.ED82.E$131.DEF25.DEFC
$102.F11.F16.E.E25.E2.C35.DE$131.DE26.DE.C35.E$130.F2.2A26.AC$133.2B
21.E4.B14C25.DE$156.DE5.AB.AB.AB.AB.A25.E$133.2A41.B$133.2B19.F21.2CA
25.DE$177.CBA.BA.BA.BA15.E$133.2A40.2A.BA.BA.BA.BA.EF$133.2B39.CB2C
11.E.E15.DEF$176.BA11.DED$117.C15.2A38.ED13.F16.BC.E.C$133.2B39.E19.E
11.CA$193.ED10.ACB$116.2A15.2A35.ED33.BC$116.2B15.2B36.E25.E8.CA$196.
ED7.ACB$105.C10.2A15.2A32.ED36.BC$115.A2B15.2B33.E28.2F.2F4.CA$107.DE
6.2C.C79.DED4.ACB$107.E8.A.C14.2A29.ED39.BC$117.BC14.2B30.E29.E7.E.CA
$110.DE6.C76.DE5.ED.C$110.E6.AC14.2A26.ED42.2F2.E$117.BC13.CB2C26.E
30.F14.ED$113.DE3.C13.C2.B$113.E3.AC13.CA24.ED52.E$117.BC40.E51.ED$
116.D.C$115.F2.C17.DE17.ED58.E$136.E19.E57.ED$14.F10.F$15.DE6.ED92.2A
20.DE11.ED64.E$15.E8.E31.F60.2B20.E13.E63.ED$19.2F36.DE27.F$18.D2.D
35.E26.ED31.2A23.DE5.ED70.E$19.2B64.E31.2B23.E7.E69.ED$15.E8.E35.DE$
15.DE2.2A2.ED35.E20.ED34.2A26.DED76.E$14.F4.2B4.F56.E31.C2.2B2.C23.E.
E75.ED$63.DE39.B.AB.AB.AB8.BA.BA.BA.BA.BA.BA.BA.BA2.F$19.2A42.E14.ED
22.C.B.AB.AB.ABC2A2C2ACBA.BA.BA.BA.BA.BA.BA.BA2.C79.E$19.2B58.E33.ACA
B2CBACA103.ED$30.FE34.DE$19.2A9.E35.E8.ED40.2A111.E$19.2B55.E40.2B
110.ED$33.DE34.DE2F$19.2A12.E35.E3.D43.2A114.E$18.CB2C33.C16.B44.2B
113.ED$18.C2.B14.DE16.BA.BA.BA.BA.BA.BA2CA.BA.BA.BA.BA.BA.BA.BA.BA.BA
.BA.BA.BA.B.C$18.CA16.E16.B.C.BA.BA.BA.BA.BA2CA.BA.BA.BA.BA.BA.BA.BA.
BA.BA.BA.BA.BA.B5.2A117.E$18.CB35.CB15.B44.2B116.ED$18.C20.DE13.CA13.
E3.D$18.CA19.E2.F26.DE2F25.F18.2A120.E$18.CB56.E18.FED19.2B119.ED$39.
E2.2A22.E8.ED20.F$21.DE16.DE.2B22.DE29.F2.E16.2A$21.E57.E13.ED4.ED16.
2B121.C$36.E5.2A19.E14.ED14.E$24.DE10.DE4.2B19.DE38.E13.2A$24.E16.B
40.E7.ED10.ED13.2B$33.E7.2CAC14.ACB19.ED8.E$27.DE4.DE6.B.AB.AB.AB.AB.
AB.ABCA44.E10.2A$27.E2.F13.C.AB.AB.AB.AB.AB25.EFED16.ED9.A2B$30.F29.C
23.EDF.E27.2C.C$30.DE52.F24.E7.A.C$29.2F56.F20.ED8.BC$119.C$112.E5.AC
$111.ED5.BC$116.C2.C$116.F.AC$114.EDF.AC$119.C$116.2F!
A diode and a controllable p4 gun:

Code: Select all

x = 119, y = 84, rule = FireWorld+old
7$80.F8$39.F3$93.F$84.F2$63.C2$89.F$88.F10.F4$28.C54.F10.F$29.BA4.A
11.BA44.FD$28.CBA16.BA4.F$28.CA29.C$27.C3.C.CBC$34.A63.F$59.CF$59.DF$
59.E$59.DF4.F$59.CF$43.2F38.C$20.C41.F8.AB10.CB$59.C11.AB10.2A$83.C4$
31.E18.F13.F$31.DE3$33.E$33.DE7$19.9C!
AND-NOT:

Code: Select all

x = 63, y = 48, rule = FireWorld+old
5$37.4C$5.C34.C$6.CA22.CA8.3C$6.CBA21.CBA.ED4.B.C$7.B5.BA4.BA4.BA4.BA
2.E.C3.AC$6.C2.22C12.12C$9.B.A.BA.BA.BA.BA.BA.B3.D13.BA4.BA$9.2B18.DF
.E$9.2C$27.F3.F$50.C$48.E$49.E3$15.C$14.2BA4.BA4.BA4.BA4.BA4.BA4.BA4.
BA2.C$15.CA4.BA4.BA4.BA4.BA.ED.BA4.BA4.BA$15.C27.E$14.C$39.ED$40.E2$
36.ED$37.E2$33.ED$29.F4.E2$21.C9.D$21.BA.BA.BA.B.F$20.ACA.BA.BA.B$20.
AC$20.CB!
AND:

Code: Select all

x = 77, y = 55, rule = FireWorld+old
10$29.FE.EF$33.E$11.2C15.C3.FD2.C$11.2A16.BA$11.AB.BA.BA.BA.BA.BA2.2C
3.BA.BA.BA.BA.BA.BA.BA.BA.BA2.C$11.22C2.BA.BA.BA.BA.BA.BA.BA.BA.BA$
11.AB.BA.BA.BA.BA.BA.BA$11.2A19.FD2.C$11.2C16.E3.E$29.FE.EF7$7.C$8.C$
8.CA4.BA4.BA$7.2BA4.BA4.BA4.EF$8.C16.E.E$25.DED$24.F6.C2$32.BA4.BA4.B
A4.BA4.BA4.BA4.B$29.ED.BA4.BA4.BA4.BA4.BA4.BA4.B.C2$24.F6.C$25.DED$8.
C16.E.E$8.BA.BA.BA.BA.BA.BA.EF$7.ACA.BA.BA.BA.BA.BA$7.AC$7.CB!
OR:

Code: Select all

x = 60, y = 63, rule = FireWorld+old
3$31.F3.F$13.2C24.4C$13.2B18.DF.EF.A2.C$13.B.A.BA.BA.BA.BA.BA.B3.DF.E
.BC$13.22C7.A9C$13.B.A.BA.BA.BA.BA.BA.B3.DF6.BA.BA.BA$13.2B18.DF.EF.C
$13.2C$31.F3.F13$13.C32.F$14.C$13.BC4.BA4.BA4.B11.ED$13.2A4.BA4.BA4.B
.F10.E$14.C17.D$40.ED$30.F10.E$37.F$37.FD$38.E$37.FD$34.ED.F$30.F4.E
5.E$40.ED$14.C$16.BA4.BA4.BA3.F10.E$14.C.BA4.BA4.BA13.ED$14.CB$13.CA
31.F!
A spontaneous breeder generator:

Code: Select all

x = 83, y = 65, rule = FireWorld+old
11$60.F2$62.F$53.F9.F2$51.F13.F2$54.2F2.F2.F$59.F$53.2FDF3.ED$55.E5.E
2$54.2F.F.F.E$55.DEDFDED3$51.E13.E$50.E.E11.ED$51.E2$47.ED$48.E2$12.C
31.ED$12.BCA30.E$11.ABCBA.BA.BA.BA.BA.BA$12.A.BA.BA.BA.BA.BA.BA.F8.ED
$13.C28.E$29.E3.E$29.FE.ED4.ED$36.F2.E$36.F$35.ED$36.F$36.F.F$29.FE.E
D$29.E3.E$13.C$12.A.BA.BA.BA.BA.BA.BA.F$11.ABCBA.BA.BA.BA.BA.BA$12.BC
A$12.C!

Yoel
Posts: 319
Joined: July 2nd, 2020, 1:02 am
Location: Electronic jungle
Contact:

Re: FireWorld+

Post by Yoel » September 25th, 2022, 4:52 am

The new definition of FireWorld+ that looks like a natural extension of FireWorld, not some artificial ad hoc construction.

It has two additional states (6 altogether): diaphotons (green) and diaphoton triggers (white). Diaphoton triggers are mostly inert like the yellow (2 generation "dying") cells. Both yellow or white cells count for birth or survival as empty.

Diaphotons allow spaceships to travel diagonally at the speed of light. A diaphoton cell never survives and is only born if it has exactly 1 diaphoton neighbor in diagonal. Cells horizontally adjacent to this diaphoton neighbor must be empty or diaphoton triggers (not yellow).Two horizontally adjacent green cells become yellow. An empty cell with exactly 1 horizontal diaphoton becomes yellow.

A red cells is born, if surrounded by 2 red of green cells in any combination in either "a" or "k" position. This generalized the original "2ak" behavior. If dying, both red and green cells become yellow (generation 2).

The wiring rule is as follows: A red (electron/photon) cell is born, if surrounded by 2 or 3 wire cells and by 1 or 2 live (red or green) cells. These 2 live cells must be in either "a" or "k" position, to match the "2ak" behavior.

One red cell and a diaphoton trigger cell give birth to a diaphoton.

Code: Select all

@RULE FireWorld+

# Copyright by Yoel Matveyev, 2022
# The GNU General Public License v3.0

# This rule is a combination of two rules: FireWorld and a variety of Diaphotons.
# The idea to combine these rules was partially inspired by Brian Prentice's rule Mites.

# FireWorld is the redefinition of the old Fireworld (03ajkr/2ak/3), proven in itself to be capable 
# of universal computation and to be suitable for constructing complex logic circuits.

# FireWorld is a hybrid rule combining 03ajkr/2ak/3 and a wiring system, in which "electrons" run
# on the wires' surface. It is fully backward compatible with the old Fireworld.

# Diaphotons is a simple rule that allows spaceships to travel diagonally at the "speed of light":
# A diaphoton cell never survives and is only born if it has exactly 1 diaphoton neighbor in diagonal;
# Cells horizontally adjacent to this diaphoton neighbor must be empty or diaphoton triggers.
# Two horizontally adjacent green cells become yellow.
# An empty cell with exactly 1 horizontal diaphoton becomes yellow.

# Being fully backward compatible with Fireworld, FireWorld adds two additional states: 
# Diaphpotons (green) and diaphoton triggers (white).

# A red cells is born, if surrounded by 2 red of green cells in any combination in either "a" or "k" position.
# This generalized the original 2ak behavior. If dying, both red and green cells become yellow (generation 2).

# As in FireWorld, wires are implemented as the fourth, immutable state 3. The wiring rule is as follows:

# A red (electron) cell is born, if surrounded by 2 or 3 wire cells and by 1 or 2 live (red or green) cells; 
# 2 live cells must be in either "a" or "k" position, to match the "2ak" behavior of Fireworld.

# A green cell is born, if an empty cell is surrounded by exactly 1 photon cell and 1 diaphoton trigger cell.

# Yellow (dying) or white (diaphoton trigger) cells count for birth or survival as empty.  

@COLORS

0 0 0 0
1 255 0 0
2 255 255 0
3 0 0 255
4 0 255 0
5 255 255 255

@TABLE

n_states:6
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1,2,3,4,5}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a

var i={0,2,5}
var j=i
var k=i
var l=i
var m=i
var n=i
var o=i
var p=i

var L={1,4}
var L2=L

var x={0,5}
var y=x

# Modified original 2001 Fireworld

0,L,L2,k,l,m,n,o,p,1
0,L,j,k,L2,m,n,o,p,1

1,i,j,k,l,m,n,o,p,1
1,1,1,1,l,m,n,o,p,1
1,1,j,1,1,m,n,o,p,1
1,1,1,k,l,1,n,o,p,1
1,1,j,1,l,m,1,o,p,1

# Diaphotons

0,x,4,y,l,m,n,o,p,4
0,4,j,k,l,m,n,o,p,2
4,4,j,k,l,m,n,o,p,2

# A computer-generated list of all possible living cells and wire cells positions

0,i,j,L,l,m,3,o,3,1
0,i,j,3,3,m,n,L,p,1
0,i,j,3,l,L,n,3,p,1
0,i,j,3,l,L,n,o,3,1
0,i,j,3,l,3,n,L,p,1
0,i,j,3,l,3,n,o,L,1
0,i,j,3,l,m,3,o,L,1
0,i,j,3,l,m,n,L,3,1
0,i,j,3,l,m,n,3,L,1
0,i,j,k,3,3,n,o,L,1
0,i,j,k,3,m,L,o,3,1
0,i,j,k,3,m,3,o,L,1
0,i,j,k,3,m,n,L,3,1
0,i,j,k,3,m,n,3,L,1
0,i,j,k,l,L,3,o,3,1
0,i,j,k,l,L,n,3,3,1
0,i,j,k,l,3,L,3,p,1
0,i,j,k,l,3,L,o,3,1
0,i,j,k,l,3,3,L,p,1
0,i,j,k,l,3,3,o,L,1
0,i,j,k,l,3,n,L,3,1
0,i,j,k,l,3,n,3,L,1
0,i,j,k,l,m,3,L,3,1
0,i,j,k,l,m,3,3,L,1

0,3,j,3,l,3,n,L,p,1
0,i,3,k,3,m,3,o,L,1
0,i,j,L,3,m,3,o,3,1
0,i,j,L,l,3,3,o,3,1
0,i,j,L,l,3,n,3,3,1
0,i,j,L,l,m,3,3,3,1
0,i,j,3,L,3,n,o,3,1
0,i,j,3,L,m,3,o,3,1
0,i,j,3,3,L,n,o,3,1
0,i,j,3,3,3,n,L,p,1
0,i,j,3,3,3,n,o,L,1
0,i,j,3,3,m,L,3,p,1
0,i,j,3,3,m,L,o,3,1
0,i,j,3,3,m,3,L,p,1
0,i,j,3,3,m,3,o,L,1
0,i,j,3,3,m,n,L,3,1
0,i,j,3,3,m,n,3,L,1
0,i,j,3,l,L,3,3,p,1
0,i,j,3,l,L,3,o,3,1
0,i,j,3,l,L,n,3,3,1
0,i,j,3,l,3,L,3,p,1
0,i,j,3,l,3,L,o,3,1
0,i,j,3,l,3,3,L,p,1
0,i,j,3,l,3,3,o,L,1
0,i,j,3,l,3,n,L,3,1
0,i,j,3,l,3,n,3,L,1
0,i,j,3,l,m,3,L,3,1
0,i,j,3,l,m,3,3,L,1
0,i,j,k,3,3,3,o,L,1
0,i,j,k,3,3,n,L,3,1
0,i,j,k,3,3,n,3,L,1
0,i,j,k,3,m,L,3,3,1
0,i,j,k,3,m,3,L,3,1
0,i,j,k,3,m,3,3,L,1
0,i,j,k,l,L,3,3,3,1
0,i,j,k,l,3,L,3,3,1
0,i,j,k,l,3,3,L,3,1
0,i,j,k,l,3,3,3,L,1

0,i,j,L,3,m,L,o,3,1
0,i,j,L,3,m,3,o,L,1
0,i,j,L,l,3,n,3,L,1
0,i,j,L,l,3,L,o,3,1
0,i,j,L,l,3,3,o,L,1
0,i,j,L,l,m,3,3,L,1
0,i,j,L,L,m,3,o,3,1
0,i,j,3,l,L,3,o,L,1
0,i,j,3,l,L,n,3,L,1
0,i,j,3,l,L,L,o,3,1
0,i,j,3,l,3,n,L,L,1
0,i,j,3,l,3,L,L,p,1
0,i,j,3,l,m,3,L,L,1
0,i,j,3,L,3,n,L,p,1
0,i,j,3,L,m,3,L,p,1
0,i,j,3,L,m,n,L,3,1
0,i,j,3,L,L,n,3,p,1
0,i,j,3,L,L,n,o,3,1
0,i,j,3,3,m,L,L,p,1
0,i,j,3,3,m,n,L,L,1
0,i,j,3,3,L,n,o,L,1
0,i,j,k,3,m,3,L,L,1
0,i,j,k,3,L,3,o,L,1
0,i,j,k,3,L,n,3,L,1
0,i,j,k,3,L,L,o,3,1
0,i,j,k,3,3,n,L,L,1
0,i,j,k,l,L,3,3,L,1
0,i,j,k,l,L,L,3,3,1
0,i,j,k,l,3,L,L,3,1
0,i,j,k,l,3,3,L,L,1

0,3,L,3,l,3,n,L,p,1
0,3,L,L,l,3,n,3,p,1
0,i,3,L,3,m,3,o,L,1
0,i,3,L,l,3,n,3,L,1
0,i,3,L,l,3,L,o,3,1
0,i,3,L,L,m,3,o,3,1
0,i,3,3,l,L,3,o,L,1
0,i,3,3,l,L,n,3,L,1
0,i,3,3,l,L,L,o,3,1
0,i,3,3,l,3,n,L,L,1
0,i,j,L,3,m,L,3,3,1
0,i,j,L,3,m,3,3,L,1
0,i,j,L,3,3,n,3,L,1
0,i,j,L,3,3,L,o,3,1
0,i,j,L,3,3,3,o,L,1
0,i,j,L,l,3,L,3,3,1
0,i,j,L,l,3,3,3,L,1
0,i,j,L,L,3,n,3,3,1
0,i,j,L,L,3,3,o,3,1
0,i,j,L,L,m,3,3,3,1
0,i,j,3,l,L,3,3,L,1
0,i,j,3,l,L,L,3,3,1
0,i,j,3,l,3,L,L,3,1
0,i,j,3,l,3,3,L,L,1
0,i,j,3,L,3,n,L,3,1
0,i,j,3,L,3,3,L,p,1
0,i,j,3,L,m,3,L,3,1
0,i,j,3,L,L,3,o,3,1
0,i,j,3,L,L,n,3,3,1
0,i,j,3,3,m,L,L,3,1
0,i,j,3,3,m,3,L,L,1
0,i,j,3,3,L,3,o,L,1
0,i,j,3,3,L,n,3,L,1
0,i,j,3,3,L,L,3,p,1
0,i,j,3,3,L,L,o,3,1
0,i,j,3,3,3,n,L,L,1
0,i,j,3,3,3,L,L,p,1
0,i,j,k,3,L,3,3,L,1
0,i,j,k,3,3,L,L,3,1
0,i,j,k,3,3,3,L,L,1

# One red cell and a diaphoton trigger cell give birth to a diaphoton.

0,5,1,k,l,m,n,o,p,4
0,1,5,k,l,m,n,o,p,4
0,5,j,1,l,m,n,o,p,4
0,i,1,k,5,m,n,o,p,4
0,1,j,k,5,m,n,o,p,4
0,5,j,k,1,m,n,o,p,4
0,5,j,k,l,1,n,o,p,4
0,i,5,k,l,m,1,o,p,4

# Cleaning up, making sure the wires are immutable

1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,0
3,a,b,c,d,e,f,g,h,3
4,a,b,c,d,e,f,g,h,0
5,a,b,c,d,e,f,g,h,5

P3+ AND and OR (very bulky in FireWorld).

Code: Select all

x = 71, y = 68, rule = FireWorld+
8$36.E$33.E$14.AC15.C.EDE.B.C$10.C3.CB18.BEBD$10.BC2A2.A.BA.BA.BA.BA.
BA.E5.BA.BA.BA.BA.BA.BA2.C$9.ABCB.20C5.BA.BA.BA.BA.BA.BA$10.A.BA2.A.B
A.BA.BA.BA.BAEB2.BD$11.C2.CB18.E2.B.C$14.AC14.C.E.E$32.EBD$35.E5$36.E
$33.E$14.AC15.C.EDE.B$10.C3.CB18.BEBD4.ACB$10.BC2A2.A.BA.BA.BA.BA.BA.
E6.C.BC.BA.BA.BA.BA2.C$9.ABCB.20C5.BA.BA.BA.BA.BA.BA$10.A.BA2.A.BA.BA
.BA.BA.BAEB2.BD2.C2.C$11.C2.CB18.E2.B$14.AC14.C.E.E$32.EBD$35.E8$14.A
C20.C2.E$10.C3.CB21.E3.C$10.BC2A2.A.BA.BA.BA.BA.BA.BA.BA$9.ABCB.24C.B
D.BA.BA.BA.BA.BA2.C$10.A.BA2.A.BA.BA.BA.BA.BA2.C4.BD.BA.BA.BA.BA.BA$
11.C2.CB17.BA2C$14.AC17.CA.B4.C$36.ED$35.C2.E7$14.AC20.C2.E$10.C3.CB
21.E6.AC$10.BC2A2.A.BA.BA.BA.BA.BA.BA.BA2.B3.BCA.BA.BA.BA2.C$9.ABCB.
24C.BD.C2.BA.BA.BA.BA$10.A.BA2.A.BA.BA.BA.BA.BA.B5.BD.BA.C$11.C2.CB
18.A2C3.B.C$14.AC17.C2.B$34.B.ED$35.C2.E!
P3+ AND-OR:

Code: Select all

x = 68, y = 27, rule = FireWorld+
5$35.C$9.BC21.C$5.CA2.C23.E$6.C2BA.BA.BA.BA.BA.BA.BA.BA.BA2.B$4.B.C2.
25C$5.BA.BA.BA.BA.BA.BA.BA.BA.BA2.A.BA.B.C$6.C2.C22.BC.BA.B$9.BC21.AC
B6.C2$41.C21.C$40.2C!
A wiring demo:

Code: Select all

x = 193, y = 121, rule = FireWorld+
15$60.E37.E$61.DB33.BD$61.B35.B2$64.DB27.BD$64.B29.B2$67.DB21.BD$67.B
23.B$115.C$70.DB15.BD$70.B17.B2$73.DB9.BD$73.B11.B20.C11.C2$76.DB3.BD
23.C11.2C.C$76.B5.B23.C2$76.C.ED39.2B$75.BA2.B39.2A$76.C.ED$72.BD40.A
$73.B2.B5.B21.2A$76.DB3.BD21.2B$69.BD$66.2C2.B2.B11.B$66.BA2.E2.DB9.B
D16.C5.C$68.C35.DBD$63.BD5.B16.BA.BA.BA.BA.BA.BAEBA4.BA4.BA4.BA11.C$
64.B5.DB15.BA.BA.BA.BA.BA.BAEBA4.BA4.BA4.BA$104.DBD$60.BD5.B16.BD16.C
5.C$61.B5.DB16.B$66.E25.C$39.CA16.BD22.BD21.2B$22.C.B.AB.AB.AB.AB.ACB
17.B23.B21.2A$24.B.AB.AB.AB.AB.AB74.2A$39.C.DB11.BD22.BD34.2B$41.B13.
B23.B39.2A$119.2B$44.DB5.BD22.BD$44.B7.B23.B29.C$106.C11.2C.C$47.DBD
22.BD$47.B.2E22.B32.C11.C2$50.DB17.BD26.A$50.B19.B24.B$96.B$53.DB11.B
D47.C$53.B13.B24.BD$93.B$56.DB5.BD$56.B7.B24.BD$90.B$59.DBD$46.C12.B.
E22.C.BD$46.BCA13.CA21.E.E$45.ABCBA.BA.BA.B.C.ACBA.BA.BA.BA2.C10.AC$
46.A.BA.BA.BA.BA.BA.BA.BA.BA.BA10.CAC$47.C11.C2.C22.B2$82.BD2.DB$83.B
2.B2$79.BD8.DB$80.B8.B2$73.C2.BD14.DB2.C$68.C8.B14.B8.C$68.BCA.C.E20.
E.C.ACB$67.ABCBA.BD20.DB.ABCBA$68.A.B.C.E20.E.C.B.A$69.C5.C18.C5.C!

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