Whoops, I don't actually update the number of artifacts to the BB count. Replacing Dematerialize with Flicker should work. Although, we still need a flashback spell, so that will lose one exilable card.
Dance of the Manse can animate our artifacts though, which is bad. Unless we somehow made it so that we could put our enchantments in the graveyard, but not our artifacts?
Oh that's good, so we can keep some enchantments then. Including Thousand-Year Storm, which is key.
It looks like leaving behind creature tokens will mess up Goblin Grenade as well. Since we can generate one creature token, we can't be able to generate more creatures for the second computation. But then I don't see how we would be able to generate a creature for the third computation. (Unless it was something like Sky Swallower.)
Edit: Okay, first proposal for a BB iteration deck:
So, we give Arcbond to Ormendahl and one of the opponent's creatures that we also give lifelink to, and both players gain around BB(X) life each time. After the computation, we can spend the life using Change of Heart to increase the instant/sorcery storm count. We can then cast Artificial Evolution via Spellweaver Volute, and we get about BB(X) copies, allowing complete freedom to switch the creature types around, since our life gain will exceed the creature count.
I guess you did mention something about creature damage - I don't think that's an issue, that will just basically give a minus on the toughness-damage counter. Since the toughness-damage total will still be on the order of BB(X), we still have freedom to choose our input, on the scale of BB(X). Trying to bounce all the opponent creatures would lose a layer, since we would need to Dematerialize the creatures and Dowsing Dagger many times.
Letting BB_1 be a standard BB function, BB_2(X) = (BB_1)^X (X), BB_3(X) = (BB_2)^X (X), and so on:
BB_1: Each time we spend a red mana to cast Seize the Day we get another combat.
BB_2: Each time we play an artifact, we can get many copies of it thanks to all the Mirrorworks tokens in play.
BB_3: Each time we tap Tolarian Academy, we get a lot of blue mana.
BB_4: Each time we tap a Swamp, we get a lot of black mana.
What are the other possibilities for sacrificing creatures for damage?
Yeah, I knew about just having to adjust the numbers, but I figured Cytoshape would be the easiest way to do so, since we would already have it in our deck. Whatever card we used to adjust the numbers, wouldn't it need to be copied to the level of the number of creatures to be able to have the next computation iterate the Busy Beaver fuction? With the Mirari / Mirror Gallery idea, we would have X possible copies of Cytoshape or whatever we were using, and we would have BB(X) creatures on the battlefield after the first computation after an update. So we would be able to adjust a small number of the creatures. Would that be enough to get to BB(BB(X))? I wouldn't think so.
Edit: Sorry, if we got rid of Opalescence, we could have one more creature, and unlimited enchantments.
Edit: So, I was thinking about how to put together a Westvale Abbey deck with BB iteration, and I got stuck on being able to recycle Spellweaver Volute. I can't figure out how to get it back without also being able to get back either global enchantments or creatures, or using a creature. jfb's idea to retrieve creatures and enchantments, and be forced to sacrifice them again, doesn't seem to work for the Westvale Abbey version, since we still have to Prince to attack with. We do have extra slots for creatures, but if we sacrifice that creature, we need to not be able to get it back again for later computations.
Edit: Ooh, maybe we can have a dummy instant, and we can just switch back and forth between Spellweaver Volute enchanting that, and the ones we care about.
Call me ambitious, but I kinda want to get layers of iteration of the Busy Beaver function.
A partial solution is to use Mirari and Mirror Gallery. That can work, but we only get a full BB iteration right after we "update" some resource that we have to the number of opponent's creatures. By contrast, if we can hit every opponent creature with Cytoshape each time we run the computation, then each update can apply BB^X (X).
Hmm, one problem with Busy Beaver iteration is, with our current "sacrifice all creatures" paradigm, we can't keep around any creatures or enchantments unless they are absolutely necessary. So for example, we won't be able to keep around Thousand-Year Storm after the first BB computation.
Edit: So, without Thousand-Year Storm sticking around for the long haul, I'm wondering how I go about resetting the opponent's battlefield so that we can compute a new Busy Beaver. We need just two Arcbonds, but then we need a huge amount of Cytoshapes. Mirrorweave seems problematic, and definitely won't work without a huge amount of Artifical Evolutions. So either way we need to make some spell or spells target all or nearly all of the opponent's creatures. Creatures like Ink-Treader Nephilim can't be allowed to hang around, so we have to use Radiate I guess? But, we can't just use Spellweaver Volute for Radiate, since we need to respond with Radiate for it to work. How do we recycle Radiate cheaply?
Interesting. Have you talked to them about the variant model?
It would be pretty cool of 12 clocks + a halting clock is enough for Turing-completeness. But, having 12 card slots for Dralnu's Crusades might put us behind what we are currently doing now. Still, being able to get rid of Opalescence means we have fewer creatures, so maybe we could go back to Skirk Volcanist or Goblin Grenade? It's worth investigating I think.
Abyssal Persecutor is okay, so long as there is no way to remove it from the battlefield. (Having an instant that can remove a creature from the battlefield would already be a problem.)
So, I think I get the idea. In order for a creature group to last an arbitrarily long time, it needs to add tokens at a rate proportional to the damage taken. But, this means that the number of creatures in the creature group grows large relative to the amount of time we have until the next batch of tokens gets created. This means that, after a point, we can't spread the damage around to avoid having a creature take the maximum amount of damage (from a certain point). Seems to make sense.
Edit: So, correct me if I'm wrong: We no longer have to worry about more than 2 Arcbonds. But, giving things flash can still be a problem, since for example if we can bounce/destroy the Coat of Arms, that will bring a halt to the computation. (That might kill everything, but we will get token creation triggers.) Being able to retrieve instants can still be a problem, if we can bring back Artificial Evolution and cast it during the computation. And having our own Bishop of Wings still allows for haltable infinites, correct?
Just noting that I don't think we need the second Mystic Repeal, since we just need to get rid of Opalescence before the TM computation starts. So, we can just use a Dematerialize.
I'm wondering if it is possible to get by with one copy of Mystic Repeal, and use Izzet Guildmage to make copies. The problem is that we need to replay Opalescence in between, which would require another card to be able to do at instant speed.
Hmm, we need to put a Dowsing Dagger into play after the first copy of Mirrorweave resolves. And if we are able to do that, we have to make sure we aren't able to do that during the execution of the computation. That's a pickle...
I was wondering of Soul Sculptor could be useful, to turn some creatures into noncreatures and hide them away from being targets. But, with needing Opalescence in order to make Dralnu's Crusade a creature, I couldn't make Soul Sculptor work.
Hmm, not being able to get back Rotlung Reanimator means that we can't get creatures back in general. Fortunately, Farrelite Priest can be fetched by Misery Charm, and Thousand-Year Storm can be fetched by Replenish. Perpetual Timepiece can be replaced by Millstone.
Oh, that's too bad about Flicker, it was looking to be just what we needed. Do you have any idea on how we can update our artifacts?
Edit: Oh, it looks like Echo Storm is just what we need.
It looks like leaving behind creature tokens will mess up Goblin Grenade as well. Since we can generate one creature token, we can't be able to generate more creatures for the second computation. But then I don't see how we would be able to generate a creature for the third computation. (Unless it was something like Sky Swallower.)
Edit: Okay, first proposal for a BB iteration deck:
2 Channel
3 Forest
4 Primal Surge
5 Dralnu's Crusade
6 Coat of Arms
7 Rotlung Reanimator
8 Arcbond
9 Artificial Evolution
10 Mirrorweave
11 Thousand-Year Storm
12 Spellweaver Volute
13 Rush of Vitality
14 Opalescence
15 Dowsing Dagger
16 Westvale Abbey
17 Armed // Dangerous
18 Defy Gravity
20 Sculpting Steel
21 Mirror of Fate
22 Perpetual Timepiece
23 Seize the Day
24 Farrelite Priest
25 Nature's Spiral
26 Change of Heart
27 Boros Signet
28 Dematerialize
29 Sage's Knowledge
30 Sage's Knowledge
31 Tolarian Academy
32 Primevals' Glorious Rebirth
33 Necrogen Spellbomb
35 Amulet of Vigor
36 Deep Reconnaissance
37 Stunted Growth
38 Azor's Gateway
39 Galvanic Key
40 Runic Repetition
41 Fervent Denial
42 Nyxbloom Ancient
18 exilable cards
So, we give Arcbond to Ormendahl and one of the opponent's creatures that we also give lifelink to, and both players gain around BB(X) life each time. After the computation, we can spend the life using Change of Heart to increase the instant/sorcery storm count. We can then cast Artificial Evolution via Spellweaver Volute, and we get about BB(X) copies, allowing complete freedom to switch the creature types around, since our life gain will exceed the creature count.
I guess you did mention something about creature damage - I don't think that's an issue, that will just basically give a minus on the toughness-damage counter. Since the toughness-damage total will still be on the order of BB(X), we still have freedom to choose our input, on the scale of BB(X). Trying to bounce all the opponent creatures would lose a layer, since we would need to Dematerialize the creatures and Dowsing Dagger many times.
Letting BB_1 be a standard BB function, BB_2(X) = (BB_1)^X (X), BB_3(X) = (BB_2)^X (X), and so on:
BB_1: Each time we spend a red mana to cast Seize the Day we get another combat.
BB_2: Each time we play an artifact, we can get many copies of it thanks to all the Mirrorworks tokens in play.
BB_3: Each time we tap Tolarian Academy, we get a lot of blue mana.
BB_4: Each time we tap a Swamp, we get a lot of black mana.
BB_5: Each time we tap Sanctum of the Sun, we get a lot of green mana.
We can exile I think 10 cards, plus the 18 at the end, for 28 usages of Sanctum of the Sun. That will take us to more than BB_6(28), I guess.
What are the other possibilities for sacrificing creatures for damage?
Yeah, I knew about just having to adjust the numbers, but I figured Cytoshape would be the easiest way to do so, since we would already have it in our deck. Whatever card we used to adjust the numbers, wouldn't it need to be copied to the level of the number of creatures to be able to have the next computation iterate the Busy Beaver fuction? With the Mirari / Mirror Gallery idea, we would have X possible copies of Cytoshape or whatever we were using, and we would have BB(X) creatures on the battlefield after the first computation after an update. So we would be able to adjust a small number of the creatures. Would that be enough to get to BB(BB(X))? I wouldn't think so.
Edit: Sorry, if we got rid of Opalescence, we could have one more creature, and unlimited enchantments.
Edit: So, I was thinking about how to put together a Westvale Abbey deck with BB iteration, and I got stuck on being able to recycle Spellweaver Volute. I can't figure out how to get it back without also being able to get back either global enchantments or creatures, or using a creature. jfb's idea to retrieve creatures and enchantments, and be forced to sacrifice them again, doesn't seem to work for the Westvale Abbey version, since we still have to Prince to attack with. We do have extra slots for creatures, but if we sacrifice that creature, we need to not be able to get it back again for later computations.
Does anyone have an idea for how to get Spellweaver Volute back? If not, I guess I will switch to the Skirk Volcanist version.
Edit: Ooh, maybe we can have a dummy instant, and we can just switch back and forth between Spellweaver Volute enchanting that, and the ones we care about.
A partial solution is to use Mirari and Mirror Gallery. That can work, but we only get a full BB iteration right after we "update" some resource that we have to the number of opponent's creatures. By contrast, if we can hit every opponent creature with Cytoshape each time we run the computation, then each update can apply BB^X (X).
Edit: So, without Thousand-Year Storm sticking around for the long haul, I'm wondering how I go about resetting the opponent's battlefield so that we can compute a new Busy Beaver. We need just two Arcbonds, but then we need a huge amount of Cytoshapes. Mirrorweave seems problematic, and definitely won't work without a huge amount of Artifical Evolutions. So either way we need to make some spell or spells target all or nearly all of the opponent's creatures. Creatures like Ink-Treader Nephilim can't be allowed to hang around, so we have to use Radiate I guess? But, we can't just use Spellweaver Volute for Radiate, since we need to respond with Radiate for it to work. How do we recycle Radiate cheaply?
It would be pretty cool of 12 clocks + a halting clock is enough for Turing-completeness. But, having 12 card slots for Dralnu's Crusades might put us behind what we are currently doing now. Still, being able to get rid of Opalescence means we have fewer creatures, so maybe we could go back to Skirk Volcanist or Goblin Grenade? It's worth investigating I think.
Edit: So, correct me if I'm wrong: We no longer have to worry about more than 2 Arcbonds. But, giving things flash can still be a problem, since for example if we can bounce/destroy the Coat of Arms, that will bring a halt to the computation. (That might kill everything, but we will get token creation triggers.) Being able to retrieve instants can still be a problem, if we can bring back Artificial Evolution and cast it during the computation. And having our own Bishop of Wings still allows for haltable infinites, correct?
Just noting that I don't think we need the second Mystic Repeal, since we just need to get rid of Opalescence before the TM computation starts. So, we can just use a Dematerialize.
I'm wondering if it is possible to get by with one copy of Mystic Repeal, and use Izzet Guildmage to make copies. The problem is that we need to replay Opalescence in between, which would require another card to be able to do at instant speed.
So, right now I'm getting:
2 Channel
3 Forest
4 Primal Surge
5 Dralnu's Crusade
6 Coat of Arms
7 Bishop of Wings
8 Arcbond
9 Artificial Evolution
10 Izzet Guildmage
11 Swarm Intelligence
12 Angel's Grace
13 Mirrorweave
14 Opalescence
15 Dowsing Dagger
16 Westvale Abbey
17 Armed // Dangerous
18 Defy Gravity
19 Quicksilver Amulet
20 Mystic Repeal
21 Mystic Repeal
22 Flicker
23 Redirect
25 Thran Dynamo
26 Sculpting Steel
27 Dematerialize
28 Sage's Knowledge
29 Sage's Knowledge
30 Tolarian Academy
31 Necrogen Spellbomb
32 Primevals' Glorious Rebirth
33 K'rrik, Son of Yawgmoth
34 Selesnya Signet
35 Energy Bolt
36 Azor's Gateway
37 Galvanic Key
38 Runic Repetition
39 Deep Reconnaissance
40 Parallel Evolution
19 Mountains
So, losing 3 Mountains takes us down to 10^^^^49.
I was wondering of Soul Sculptor could be useful, to turn some creatures into noncreatures and hide them away from being targets. But, with needing Opalescence in order to make Dralnu's Crusade a creature, I couldn't make Soul Sculptor work.
Oh, but how about this: Use a Quicksilver Amulet to put Hunted Phantasm into play, aided by a gajillion Panharmonicons. That will give the opponent the creatures we need. The plan we have uses Swarm Intelligence, so we would have to get rid of K'rrik, Son of Yawgmoth for this to work.
Edit: Ooh nice, we can only use Flicker while Izzet Guildmage is around, which is before the computation. That seems better than giving up K'rrik.