EdPeggsBusyBeaverTurmiteChallenge - GollyGang/ruletablerepository GitHub Wiki

Ed Pegg Jr's Busy Beaver Turmite Challenge

What turmite runs the longest before becoming predictable?

Current Status

2-color 3-color 4-color 5-color 6-color
1-state 9,977 steps
{{{1,2,0}, {0,8,0}}}
Langton's Ant		 67,620,060 +10 steps
{{{1,2,0}, {2,1,0}, {0,4,0}}}
Hutton/Pegg
9 unresolved 		96,557,145,085 steps
{{{1,4,0}, {2,1,0}, {3,2,0}, {0,4,0}}}
Rosie Fay
91 unresolved 		~217,782,000,000 steps
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,4,0}, {0,8,0}}}
Ed Pegg Jr
612 unresolved 		~10,660,000,000,000 steps
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,4,0}, {5,4,0}, {0,8,0}}}
CatsAreFluffy
2-state 9,533,133,147,000 +2,000 steps
{{{0,1,1}, {0,4,0}},
{{1,4,0}, {1,2,1}}}
Mark Jeronimus
570 unresolved 		1.9*10^61 steps
{{{1,1,1}, {0,8,1}, {1,1,0}},
{{2,8,0}, {1,1,0}, {1,1,1}}}
Georgi Gochev		 ??? ??? ???
3-state ??? ??? ??? ??? ???
4-state ??? ??? ??? ??? ???

Resolved Turmites

Resolved 1-state 3-color relative movement turmites

Turmites (1-state 3-color) that last more than 2 million steps. There are 9 unresolved 1s3c turmites.

code outcome image
{{{1,2,0}, {2,1,0}, {0,4,0}}} Highway at 67,620,060 +10
by Hutton/Pegg
{{{1,4,0}, {2,2,0}, {1,8,0}}} Langton switchback at 18,492,093
by Ed Pegg Jr
{{{1,2,0}, {2,4,0}, {0,8,0}}} Highway at 2,670,085
by Ed Pegg Jr

Resolved 1-state 4-color relative movement turmites

Turmites (1-state 4-color) that last more than a billion steps, or that have interesting behavior (high-period highways, traps/wedges, islands, nice patterns). There are 91 unresolved 1s4c turmites.

code outcome image
{{{1,4,0}, {2,2,0}, {3,8,0}, {0,8,0}}} Highway at 6,650,200,000
by Georgi Gochev
{{{1,2,0}, {2,8,0}, {3,1,0}, {1,4,0}}} Wedge at 5,928,300,000
by Georgi Gochev
{{{1,4,0}, {2,2,0}, {3,2,0}, {2,8,0}}} Highway at 4,915,000,000
by Georgi Gochev
{{{1,2,0}, {2,4,0}, {3,2,0}, {3,1,0}}} Dual Highway at 4,391,220,000 +10000
by Dean Hickerson
{{{1,2,0}, {2,4,0}, {3,4,0}, {0,8,0}}} Highway at 1,589,104,000 +1,000
{{{1,4,0}, {2,2,0}, {3,8,0}, {0,2,0}}} Highway at 1,468,709,000 +1000
by Ed Pegg Jr
{{{1,2,0}, {2,4,0}, {3,2,0}, {0,1,0}}} Highway at 1,167,460,000
by Georgi Gochev
{{{1,2,0}, {2,2,0}, {3,4,0}, {0,8,0}}} Period-185,236 highway at 255,062,383
By Ed Pegg Jr
{{{1,2,0}, {2,2,0}, {3,4,0}, {0,4,0}}} Period-327,776 highway at 148,555,690
By Ed Pegg Jr
{{{1,2,0}, {2,2,0}, {3,2,0}, {1,8,0}}} Period-964 highway, saltus 6,6, at 23,954,482,122
by Rosie Fay
{{{1,4,0}, {2,1,0}, {3,2,0}, {0,4,0}}} Period-174 highway, saltus -2,0, at 96,557,145,085
by Rosie Fay

Resolved 1-state 5-color relative movement turmites

Turmites (1-state 5-color) that last more than a billion steps, or that have interesting behavior (high-period highways, traps/wedges, islands, nice patterns). There are 574 unresolved turmites listed at the subpage, UnresolvedTurmites1States5Colors.

code outcome image
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,4,0}, {0,8,0}}} Highway at 217,782,000,000 +10,000,000
by Ed Pegg Jr
Part of Langton's Ant series
{{{1,4,0}, {2,2,0}, {3,8,0}, {4,8,0}, {3,2,0}}} highway at 869,794,833
by Ed Pegg Jr
{{{1,2,0}, {2,2,0}, {3,4,0}, {4,2,0}, {4,1,0}}} double highway at 775,686,809
by Ed Pegg Jr
{{{1,2,0}, {2,2,0}, {3,4,0}, {4,1,0}, {0,1,0}}} highway 499,990,000
by Ed Pegg Jr
{{{1,2,0}, {2,1,0}, {3,2,0}, {4,8,0}, {0,4,0}}} highway at 485,664,513
by Ed Pegg Jr
{{{1,4,0}, {2,1,0}, {3,2,0}, {4,1,0}, {2,4,0}}} highway at 148,978,433
by Ed Pegg Jr
{{{1,2,0}, {2,1,0}, {3,4,0}, {4,4,0}, {4,1,0}}} double highway at 136,800,000
by Georgi Gochev
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,2,0}, {1,8,0}}} trap at 35,300,000
by Ed Pegg Jr
{{{1,2,0},{2,1,0},{3,2,0},{4,8,0},{2,2,0}}} highway at 1301538189, period 98, saltus 0,2
by Rosie Fay
{{{1,2,0},{2,1,0},{3,4,0},{4,1,0},{2,2,0}}} highway at 276757358, period 88, saltus 2,0
by Rosie Fay
{{{1,2,0},{2,1,0},{3,4,0},{4,1,0},{3,2,0}}} highway at 2002120074, period 144, saltus 0,-2
by Rosie Fay
{{{1,2,0},{2,1,0},{3,8,0},{4,2,0},{4,1,0}}} highway at 5472298682, period 42, saltus -1,-1
by Rosie Fay
{{{1,2,0},{2,2,0},{3,1,0},{4,8,0},{0,1,0}}} highway at 1441545729, period 96, saltus -2,2
by Rosie Fay
{{{1,2,0},{2,2,0},{3,2,0},{4,1,0},{0,8,0}}} highway at 7071821517, period 1519, saltus 6,13
by Rosie Fay
{{{1,2,0},{2,2,0},{3,2,0},{4,4,0},{1,8,0}}} highway at 3281052733, period 140, saltus 0,2
by Rosie Fay
{{{1,2,0},{2,2,0},{3,2,0},{4,8,0},{0,2,0}}} highway at 8817704078, period 332, saltus -2,2
by Rosie Fay
{{{1,2,0},{2,2,0},{3,2,0},{4,8,0},{1,1,0}}} highway at 231822155, period 112, saltus -2,0
by Rosie Fay
{{{1,2,0},{2,2,0},{3,4,0},{4,8,0},{0,8,0}}} highway at 74190635, period 80, saltus -2,0
by Rosie Fay
{{{1,2,0},{2,2,0},{3,8,0},{4,2,0},{1,1,0}}} highway at 169779758, period 92, saltus 2,0
by Rosie Fay
{{{1,2,0},{2,4,0},{3,1,0},{4,1,0},{3,8,0}}} highway at 9772987, period 49, saltus -2,1
by Rosie Fay
{{{1,2,0},{2,4,0},{3,1,0},{4,4,0},{0,1,0}}} highway at 138843634, period 124, saltus 0,2
by Rosie Fay
{{{1,2,0},{2,4,0},{3,2,0},{4,2,0},{1,8,0}}} highway at 2412646, period 110, saltus 2,0
by Rosie Fay
{{{1,2,0},{2,4,0},{3,4,0},{4,8,0},{0,2,0}}} highway at 1002391344, period 4953, saltus 12,-17
by Rosie Fay
{{{1,2,0},{2,4,0},{3,8,0},{4,2,0},{0,2,0}}} highway at 9731529411, period 179, saltus 2,1
by Rosie Fay
{{{1,2,0},{2,8,0},{3,2,0},{4,4,0},{0,4,0}}} highway at 4893974676, period 322274, saltus -107,9
by Rosie Fay
{{{1,2,0},{2,8,0},{3,2,0},{4,4,0},{1,1,0}}} highway at 11955373, period 76, saltus 2,0
by Rosie Fay
{{{1,2,0},{2,8,0},{3,4,0},{4,2,0},{0,2,0}}} highway at 272516201, period 106, saltus 0,-2
by Rosie Fay
{{{1,2,0},{2,8,0},{3,4,0},{4,4,0},{1,1,0}}} highway at 733269276, period 208, saltus 2,0
by Rosie Fay
{{{1,4,0},{2,1,0},{3,1,0},{4,1,0},{2,2,0}}} highway at 8708075614, period 53, saltus -1,0
by Rosie Fay
{{{1,4,0},{2,1,0},{3,1,0},{4,2,0},{2,8,0}}} highway at 11283153, period 33, saltus -1,0
by Rosie Fay
{{{1,4,0},{2,2,0},{3,1,0},{4,1,0},{0,8,0}}} highway at 3130206318, period 94, saltus 0,2
by Rosie Fay
{{{1,4,0},{2,2,0},{3,1,0},{4,8,0},{2,8,0}}} highway at 7486624993, period 162, saltus 0,-2
by Rosie Fay
{{{1,4,0},{2,2,0},{3,2,0},{4,1,0},{0,2,0}}} highway at 66301186, period 102, saltus 2,0
by Rosie Fay
{{{1,4,0},{2,2,0},{3,2,0},{4,1,0},{1,8,0}}} highway at 4925873, period 78, saltus -2,0
by Rosie Fay
{{{1,4,0},{2,2,0},{3,2,0},{4,8,0},{0,4,0}}} highway at 28208033, period 190, saltus 0,2
by Rosie Fay
{{{1,4,0},{2,2,0},{3,4,0},{4,2,0},{1,1,0}}} highway at 512935190, period 396, saltus -3,3
by Rosie Fay
{{{1,4,0},{2,2,0},{3,4,0},{4,8,0},{1,8,0}}} highway at 238613221, period 144, saltus 2,0
by Rosie Fay
{{{1,4,0},{2,4,0},{3,2,0},{4,1,0},{0,4,0}}} highway at 119832858, period 270, saltus -2,0
by Rosie Fay
{{{1,4,0},{2,4,0},{3,2,0},{4,1,0},{3,8,0}}} highway at 119950543, period 57, saltus -1,0
by Rosie Fay
{{{1,4,0},{2,4,0},{3,2,0},{4,2,0},{0,8,0}}} highway at 928283721, period 248, saltus 0,-2
by Rosie Fay
{{{1,2,0},{2,1,0},{3,2,0},{4,4,0},{3,1,0}}} double highway at ~3423000
by Rosie Fay
{{{1,2,0},{2,1,0},{3,2,0},{4,8,0},{4,1,0}}} double highway at ~653M
by Rosie Fay
{{{1,2,0},{2,1,0},{3,8,0},{4,1,0},{3,4,0}}} double highway at ~45M
by Rosie Fay
{{{1,2,0},{2,1,0},{3,8,0},{4,4,0},{1,1,0}}} wedge at ~21M
by Rosie Fay
{{{1,2,0},{2,2,0},{3,2,0},{4,8,0},{4,1,0}}} double highway at ~4283M
by Rosie Fay
{{{1,2,0},{2,4,0},{3,1,0},{4,1,0},{1,1,0}}} double highway at ~730M
by Rosie Fay
{{{1,2,0},{2,4,0},{3,2,0},{4,1,0},{3,1,0}}} double highway at ~4391M
by Rosie Fay
{{{1,2,0},{2,4,0},{3,8,0},{4,8,0},{1,8,0}}} diamond at 0
by Rosie Fay
{{{1,2,0},{2,8,0},{3,2,0},{4,1,0},{3,4,0}}} double highway at ~155M
by Rosie Fay

Resolved 2-state 2-color relative movement turmites

Turmites (2-state 2-color) that last more than a billion steps, or that have interesting behavior (high-period highways, traps/wedges, islands, nice patterns). There are 570 unresolved 2c2c turmites.

code outcome image
{{{0,1,1}, {0,4,0}}, {{1,4,0}, {1,2,1}}}

{{{1,4,0}, {0,1,1}}, {{0,4,0}, {1,2,1}}} 		Highway at 9,533,133,147,000 +2,000
by Mark Jeronimus
{{{1,2,0}, {0,1,1}}, {{0,2,0}, {1,2,1}}} Highway at 3,511,330,000,000 +10,000,000
First time highway detected at 39 millions.
by Georgi Gochev
{{{1,2,1}, {0,8,1}}, {{1,8,1}, {0,1,0}}} Highway at 8,362,028,000 +1000
by Mark Jeronimus.
Slightly modified version of a rule by Georgi Gochev
{{{1,2,1}, {0,8,0}}, {{1,2,0}, {0,1,0}}}
Mirror version:
{{{1,8,1}, {0,2,0}}, {{1,8,0}, {0,1,0}}} 		Wedge at 7,734,883,000 +1,000
By Georgi Gochev
{{{0,2,1}, {1,2,0}}, {{1,8,1}, {0,4,0}}} Highway at 3,133,860,000 +10,000
by Ed Pegg Jr
{{{0,4,1}, {0,1,1}}, {{1,2,1}, {0,1,0}}}
Rotated version:
{{{1,2,0}, {0,1,1}}, {{0,4,0}, {0,1,0}}} 		Trapped at 1,457,592,964 +2
by Mark Jeronimus
{{{0,1,1}, {1,1,1}}, {{1,2,0}, {0,1,1}}}
{{{1,2,1}, {0,1,0}}, {{0,1,0}, {1,1,0}}} 		Highway at 1,368,150,000 +1,000
by Mark Jeronimus
{{{1,2,1}, {0,2,0}}, {{1,1,0}, {1,8,0}}} Highway at 1,347,724,200 +1,000
by Mark Jeronimus
{{{1,4,0}, {0,2,1}}, {{1,1,0}, {0,1,1}}} Highway at 1,229,154,000 +1,000
by Mark Jeronimus
{{{1,2,0}, {0,8,1}}, {{1,8,0}, {1,2,0}}}
Mirrored version:
{{{1,2,1}, {1,8,1}}, {{1,8,1}, {0,2,0}}} 		Trapped at 1,119,960,690 +100
by Mark Jeronimus
{{{1,2,1}, {0,1,1}}, {{1,2,0}, {0,8,1}}}
Mirror version:
{{{1,8,1}, {0,1,1}}, {{1,8,0}, {0,2,1}}} 		wedge at 838,149,257
{{{1,1,1}, {0,2,1}}, {{1,2,1}, {0,1,0}}}
Mirrored version:
{{{1,1,1}, {0,8,1}}, {{1,8,1}, {0,1,0}}}
Rotated version:
{{{1,2,0}, {0,1,1}}, {{1,1,0}, {0,2,0}}}
Rotated mirrored version:
{{{1,8,0}, {0,1,1}}, {{1,1,0}, {0,8,0}}} 		Double highway at 238,951,300 +100
By Georgi Gochev
{{{0,1,1}, {1,2,0}}, {{1,2,0}, {0,2,1}}}
{{{1,2,1}, {0,2,0}}, {{0,1,0}, {1,2,1}}} 		Spiral after chaos,
at 140,900,000 +100,000
Independently by Ed Pegg Jr and Mark Jeronimus
{{{1,2,1}, {0,8,1}}, {{1,4,0}, {1,1,0}}}
{{{1,4,1}, {1,1,1}}, {{1,2,0}, {0,8,0}}} 		Langton switchback at 70,500,000 +100,000
By Georgi Gochev
{{{1,2,1}, {0,4,0}}, {{0,1,0}, {1,1,1}}}
{{{0,1,1}, {1,1,0}}, {{1,2,0}, {0,4,1}} 		wedge at 67,689,229
{{{1,2,0}, {1,4,1}}, {{1,1,0}, {0,4,1}}} Highway at gen 63,278,000 +1000
(Period = 87512)
by Ed Pegg Jr
{{{1,4,1}, {0,1,0}}, {{1,2,0}, {1,1,1}}} Double highway at 36,104,340 +20
This rule produces islands
connected to the mainland by highways, but, by 36M generations, the mainland has grown to reach the islands.
by Mark Jeronimus
{{{0,2,1}, {1,1,0}}, {{1,1,0}, {1,1,1}}} Quadruple highway at 1,799,000 +1,000
Likes quadruple highways
by Ed Pegg
{{{1,2,1}, {0,8,1}}, {{1,2,1}, {1,1,0}}}
{{{1,2,0}, {1,1,1}}, {{1,2,0}, {0,8,0}}} 		Trapped in a complex shape at 1,132,000 +1000
An exhaustive search indicates this is the most
complex trap possible for all 2s2c turmites
starting in an empty world, and up to 10 billion
gens. by Mark Jeronimus

Resolved 2-state 3-color relative movement turmites

code outcome image
{{{1,1,1}, {0,8,1}, {1,1,0}}, {{2,8,0}, {1,1,0}, {1,1,1}}} Diagonal highway at 1.9*10^61 steps
(19 333 473 344 990 976 752
614 231 423 479 612 677 954
364 906 857 285 205 055 952)
by Georgi Gochev

Langton's Ant Series

Does anyone understand why these work? Can someone calculate numbers for more in the series?

{{{1,2,0}, {0,8,0}}} Langton's Ant: 9,977 steps before making a highway. Best known for 1s2c
{{{1,2,0}, {2,4,0}, {0,8,0}}} Highway at 2,670,085
by Ed Pegg Jr 		Beaten by 2 other 1s3c turmites
{{{1,2,0}, {2,4,0}, {3,4,0}, {0,8,0}}} Highway at 1,589,104,000 +1,000
by Ed Pegg Jr 		Beaten by 4 other 1s4c turmites
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,4,0}, {0,8,0}}} Highway at 217,782,000,000 +10,000,000
by Ed Pegg Jr 		Best known for 1s5c
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,4,0}, {5,4,0}, {0,8,0}}} Highway at 10,660,000,000,000 +7,688,209,095
by CatsAreFluffy 		Best known for 1s6c
{{{1,2,0}, {2,4,0}, {3,4,0}, {4,4,0}, {5,4,0}, {6,4,0}, {0,8,0}}} Highway at 263,760,000,000,000 +7,447,861,499
by CatsAreFluffy 		Best known for 1s6c

Unresolved Turmites

Unresolved 1-state 3-color relative movement turmites

There are currently 9 unresolved 1-state 3-color turmites. The image below shows the state of the first eight rules after 20 million steps.

{{{1,2,0}, {2,1,0}, {0,8,0}}} Still chaotic at 10 billion steps.
{{{1,2,0}, {2,1,0}, {1,8,0}}} Still chaotic at 749,869,528,065
See also: {{{1,2,0}, {2,1,0}, {3,8,0}, {2,1,0}}}
{{{1,2,0}, {2,2,0}, {1,8,0}}} Still chaotic at 10 billion steps.
See also: {{{1,2,0}, {2,2,0}, {3,8,0}, {2,2,0}}}
{{{1,2,0}, {2,8,0}, {0,2,0}}} Still chaotic at 10 billion steps.
{{{1,2,0}, {2,8,0}, {0,8,0}}} Still chaotic at 10 billion steps.
{{{1,2,0}, {2,8,0}, {1,1,0}}} Still chaotic at 10 billion steps.
See also: {{{1,2,0}, {2,8,0}, {3,1,0}, {2,8,0}}}
{{{1,4,0}, {2,1,0}, {0,2,0}}} Still chaotic at 10 billion steps.
{{{1,4,0}, {2,2,0}, {0,1,0}}} Still chaotic at 10 billion steps.
{{{1,4,0}, {2,2,0}, {1,1,0}}} Binary counting highways at 2,717,308,080 +10 and at ~10 trillion steps but expected to be unpredictable again after that -- Tim Hutton
See also: {{{1,4,0}, {2,2,0}, {3,1,0}, {2,2,0}}}

Unresolved 1-state 4-color relative movement turmites

There are currently 94 unresolved 1s4c turmites. Behavior is still chaotic after the given number of steps run. If you run any of these for longer, and they don't resolve, put in your number of steps.

The population numbers are not the same as the area (number of unique visited cells), and as such will be on average 25% too low if a rule creates cells of state 0 within it's hull.

All have been run to at least 100,000,000,000 generations or until resolved. x,y coordinates below are with respect to a turmite which starts facing 1,0.

code steps run notes
{{{1,2,0}, {2,1,0}, {3,1,0}, {0,8,0}}} Still chaotic at 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,1,0}, {1,8,0}}} Still chaotic at 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,1,0}, {2,8,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,2,0}, {0,4,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,2,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,2,0}, {1,4,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,2,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,4,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,4,0}, {0,2,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,4,0}, {0,4,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,4,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,4,0}, {1,1,0}}} 4,000,000,000,000 "Submarine Turmite"

-- Population 2106 -- very slow growth, internal slow Turing machine
{{{1,2,0}, {2,1,0}, {3,4,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {0,2,0}}} Still chaotic at 509,528,543,745
Area = ~209,799,168
{{{1,2,0}, {2,1,0}, {3,8,0}, {0,4,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {1,2,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {1,4,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {1,8,0}}} 1,180,000,000,000 Lots of ternary counting.
{{{1,2,0}, {2,1,0}, {3,8,0}, {2,2,0}}} 100,000,000,000
{{{1,2,0}, {2,1,0}, {3,8,0}, {3,1,0}}} 100,000,000,000 At ~24,188,000,000, starts building 2 diametrically opposed wedges.
{{{1,2,0}, {2,2,0}, {3,1,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,1,0}, {1,4,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,1,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,1,0}, {2,4,0}}} 100,000,000,000 After ~90,600,000,000, builds 2 diametrically opposed highways. One is 5 wide and has rows of periods 1, 3, 5; 2/3 of the y=+1 row is always irregular. The other is 11 wide and has rows of periods 1, 2, 4, 6; half of the y=+1 row is always irregular.
{{{1,2,0}, {2,2,0}, {3,1,0}, {2,8,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,2,0}, {1,8,0}}} 100,000,000,000 Highway, preperiod 23954482122; period 964; saltus 6,6.
{{{1,2,0}, {2,2,0}, {3,2,0}, {2,8,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,4,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,4,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,8,0}, {0,8,0}}} 100,000,000,000
symmetric, well-known rule
{{{1,2,0}, {2,2,0}, {3,8,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,8,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,8,0}, {2,1,0}}} 100,000,000,000
{{{1,2,0}, {2,2,0}, {3,8,0}, {3,1,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,1,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,1,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,1,0}, {2,8,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,2,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,2,0}, {2,1,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,4,0}, {0,2,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,8,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,8,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,4,0}, {3,8,0}, {2,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,1,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,1,0}, {0,2,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,1,0}, {0,4,0}}} Still chaotic at 100,000,000,000
Area = ~16,608,000
{{{1,2,0}, {2,8,0}, {3,1,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,1,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,1,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {0,2,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {0,4,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {1,2,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {1,8,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {2,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,2,0}, {3,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,4,0}, {0,2,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,4,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {0,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {0,2,0}}} Still chaotic at 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {0,4,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {0,8,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {1,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {1,2,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {2,1,0}}} 100,000,000,000
{{{1,2,0}, {2,8,0}, {3,8,0}, {2,2,0}}} 100,000,000,000
{{{1,4,0}, {2,1,0}, {3,1,0}, {0,2,0}}} 100,000,000,000
{{{1,4,0}, {2,1,0}, {3,1,0}, {1,2,0}}} 100,000,000,000
{{{1,4,0}, {2,1,0}, {3,1,0}, {2,2,0}}} 1,816,220,995,841
Binary counting, makes width-4 extrusions out of the main hull;
see bottom at gens 41633 to 42084. -- Dean Hickerson
First big counter: ? - 803.43 billion.
Second big counter: 1.3~1.4 trillion - 1.600 trillion.
Third big counter: ~1.75 trillion - ~1.763 trillion.
Fourth big counter: ~1.78 trillion - (expected) 7*1033.
Short counters are easily spotted in the cell visit count map
{{{1,4,0}, {2,1,0}, {3,2,0}, {0,1,0}}} 100,000,000,000
{{{1,4,0}, {2,1,0}, {3,2,0}, {0,2,0}}} 100,000,000,000
{{{1,4,0}, {2,1,0}, {3,2,0}, {0,4,0}}} 100,000,000,000 Highway, preperiod 96557145085; period 174; saltus -2,0.
{{{1,4,0}, {2,1,0}, {3,2,0}, {1,1,0}}} 100,000,000,000
{{{1,4,0}, {2,1,0}, {3,2,0}, {1,2,0}}} 14,310,000,000,000 (click for counting details)
This rule loves ternary counters inside it's hull.
First counter: from ~2,871,000 to ~1,868,000,000.
Second counter: from 1,870,924,000 to (projected) 14.6 trillion.
{{{1,4,0}, {2,1,0}, {3,2,0}, {1,4,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,1,0}, {0,1,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,1,0}, {0,2,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,1,0}, {1,1,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,1,0}, {1,2,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,1,0}, {1,4,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,2,0}, {0,1,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,2,0}, {0,8,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,2,0}, {1,8,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,4,0}, {1,1,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,8,0}, {1,2,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,8,0}, {1,8,0}}} 100,000,000,000
{{{1,4,0}, {2,2,0}, {3,8,0}, {2,1,0}}} 100,000,000,000
{{{1,4,0}, {2,4,0}, {3,2,0}, {0,1,0}}} 100,000,000,000
{{{1,4,0}, {2,4,0}, {3,2,0}, {1,1,0}}} 100,000,000,000
{{{1,4,0}, {2,4,0}, {3,2,0}, {2,1,0}}} 100,000,000,000

Unresolved 1-state 5-color relative movement turmites

There are 612 turmites listed at UnresolvedTurmites1States5Colors.

I've run the first six of the list for 20 trillion steps. Here's step 20 trillion, and 20T+1. At around 21.5 trillion, I had a power failure.
CatsAreFluffy ran those six for around 852 trillion steps.

{{{1,2,0}, {2,2,0}, {3,4,0}, {4,4,0}, {4,1,0}}} still working after 1 trillion

Unresolved 2-state 2-color relative movement turmites

The list of 570 2s2c turmites is at UnresolvedTurmites2States2Colors. All have been run to 1.6 billion steps. Listed below are interesting runs for over 500 billion, all others should go to the subpage.

{{{1,2,0}, {1,8,1}}, {{1,8,1}, {0,8,0}}} Still chaotic at 1,021,280,049,658
Area = ~209,174,272
{{{1,2,1}, {0,4,0}}, {{1,8,1}, {1,8,0}}} Still chaotic at 567,287,499,009
Area = ~216,398,592
{{{1,2,1}, {0,2,0}}, {{1,4,1}, {0,1,0}}} Still chaotic at 305,795,580,179
Area = ~180,359,552
{{{1,1,1}, {0,2,0}}, {{1,2,0}, {0,1,1}}} Still chaotic at 113,486,027,265
Area = ~175,178,368
{{{1,2,1}, {1,8,1}}, {{1,1,0}, {0,4,0}}} Still chaotic at 21,536,408,833
Makes highways within it's hull, then corrupts them.
by Mark Jeronimus
{{{0,4,1}, {0,4,1}}, {{1,2,1}, {0,2,0}}}
Rotated version:
{{{1,2,0}, {0,2,1}}, {{0,4,0}, {0,4,0}}} 		Still chaotic at 41,759,302,342 (when its range was x=-15128~21201 y=-15935~13083, if started facing 1,0).
Maze-like and fractal-like structures.
The maze corridors are actually highways allowing
the turmite to travel vast distances surprisingly fast for a turmite with no "straight forward/no turn" rule.
by Mark Jeronimus. Also ran to 9 billion by Ed Pegg.
{{{0,2,1}, {0,2,1}}, {{1,2,0}, {1,8,1}}} Still chaotic at 100,000,000,000, at which time its area is 37422 and its range is x=-119~110 y=-112~109.
Slowest growing rule by a long shot.
Growth ratio, approx: 2700*ln(x/168000)
by Mark Jeronimus
{{{0,1,1}, {0,4,0}}, {{1,2,0}, {1,4,1}}}
{{{0,1,1}, {0,4,0}}, {{1,8,0}, {1,4,1}}}
{{{0,2,1}, {1,4,0}}, {{1,4,1}, {0,1,0}}}
{{{0,8,1}, {1,4,0}}, {{1,4,1}, {0,1,0}}}
{{{1,2,1}, {1,4,0}}, {{0,1,0}, {0,4,1}}}
{{{1,4,0}, {0,1,1}}, {{0,2,0}, {1,4,1}}}
{{{1,4,0}, {0,1,1}}, {{0,8,0}, {1,4,1}}}
{{{1,8,1}, {1,4,0}}, {{0,1,0}, {0,4,1}}}
'Oddly' rotated versions:
{{{0,1,1}, {1,4,0}}, {{1,4,1}, {0,2,0}}}
{{{0,1,1}, {1,4,0}}, {{1,4,1}, {0,8,0}}}
{{{0,2,1}, {0,4,0}}, {{1,1,0}, {1,4,1}}}
{{{0,8,1}, {0,4,0}}, {{1,1,0}, {1,4,1}}}
{{{1,1,1}, {1,4,0}}, {{0,2,0}, {0,4,1}}}
{{{1,1,1}, {1,4,0}}, {{0,8,0}, {0,4,1}}}
{{{1,4,0}, {0,2,1}}, {{0,1,0}, {1,4,1}}}
{{{1,4,0}, {0,8,1}}, {{0,1,0}, {1,4,1}}} 		Infinitely growing spiral with constantly
changing random interior.
by Mark Jeronimus
Ed Pegg says -- I don't think this
one counts as resolved, unless there is a proof.
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