A collection of (at least somewhat good) Custom Modes made since v2.0's release.
1705, but it starts with 1+1+1=3 instead of 1+1=2
Suggested by Michael Darrow, created by MathCookie
@2048PowCompCustom|2.0|W1sxLDkyXSxbMyw4XV0=|W1sxLFsxLDEsMCwxXSxbW3RydWUsMF0sW3RydWUsMF1dLFtbdHJ1ZSwxXV1dLFsxLFsyLDIsMCwxXSxbW3RydWUsLTFdLFt0cnVlLC0xXV0sW1t0cnVlLDFdXV0sWzEsWzMsIkBJbmZpbml0eSIsMCwxXSxbW3RydWUsLTFdLFt0cnVlLC0yXV0sW1t0cnVlLDFdXV1d|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|W1siQGxpbmVhci1ncmFkaWVudCIsMCxbMF0sW1siQEhTTEEiLDc5LDMxLDc2LDFdXV0sWyJAcmFkaWFsLWdyYWRpZW50IiwwLFswLDE1MF0sW1siQEhTTEEiLDkwLDEwMCwzMCwxXSxbIkBIU0xBIiwwLDEwMCwxMDAsMV1dXSxbIkBsaW5lYXItZ3JhZGllbnQiLDAsWzBdLFtbIkBIU0xBIiw3NywyMSw2OSwxXV1dLFsiQGxpbmVhci1ncmFkaWVudCIsMCxbMF0sW1siQEhTTEEiLDgyLDksNTIsMV1dXSxbIkBsaW5lYXItZ3JhZGllbnQiLDAsWzBdLFtbIkBIU0xBIiw4NSwxMiwxOSwxXV1dXQ==|WzEsMTNd|WzBd|WyJUcmlib25hY2NpIFNlcXVlbmNlIHN0YXJ0aW5nIHdpdGggMSsxKzEiLCIyMjA5IiwiTWVyZ2VzIG9jY3VyIGJldHdlZW4gdGhyZWUgMXMsIGJldHdlZW4gdHdvIDFzIGFuZCBhIDMsIG9yIGJldHdlZW4gYW55IHRpbGUgYWJvdmUgMywgdGhlIHRpbGUgYmVmb3JlIGl0LCBhbmQgdGhlIHRpbGUgdHdvIGJlZm9yZSBpdC4gR2V0IHRvIHRoZSAyMjA5IHRpbGUgdG8gd2luISJd|
2048, but tiles come in two colors, and they can only merge if they're opposite colors. The color of the resulting tile is the color of the tile being collided into.
Suggested by Michael Darrow, created by MathCookie
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AwLDcwLDFdXV0sWyJAbGluZWFyLWdyYWRpZW50IiwwLFswXSxbWyJASFNMQSIsNTUsNTAsODAsMV1dXSxbIkBsaW5lYXItZ3JhZGllbnQiLDAsWzBdLFtbIkBIU0xBIiw0MCw1MCw1NSwxXV1dLFsiQGxpbmVhci1ncmFkaWVudCIsMCxbMF0sW1siQEhTTEEiLDUwLDcwLDEwLDFdXV1d|WzEsMjMsMjRd|WzBd|WyIiLCJCaWNvbG9yIDIwNDgiLCIyMDQ4LCBidXQgdGlsZXMgY29tZSBpbiB0d28gY29sb3JzLCBhbmQgdGhleSBjYW4gb25seSBtZXJnZSBpZiB0aGV5JiN4Mjc7cmUgb3Bwb3NpdGUgY29sb3JzLiBUaGUgY29sb3Igb2YgdGhlIHJlc3VsdGluZyB0aWxlIGlzIHRoZSBjb2xvciBvZiB0aGUgdGlsZSBiZWluZyBjb2xsaWRlZCBpbnRvLiIsNF0=|
A power of two can merge with a tile 1 less than it or itself.
Created by Michael Darrow
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Two or three tiles of the same "tier" can merge. Merging two tiles increases the tier by 1, merging three tiles increases the tier by 2.
Created by Michael Darrow
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Merges occur between two equal tiles and one of the tile before them, or between three 1s. The resulting tile is two tiles later than the equal tiles.
Created by Michael Darrow
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If a tile is a multiple of 3, it merges with a 1. If a tile is 1 more than a multiple of 3, it merges with a tile that's equal to itself. If a tile is 2 more than a multiple of 3, it merges with a tile that's half of itself.
Created by Michael Darrow
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2048, but tiles come in two colors, red and green. After each turn, all tiles swap their color. Two tiles can only merge if they're both currently green.
Created by MathCookie
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Two equal tiles merge. There are junk tiles which can be destroyed by moving two tiles that are about to merge onto it.
Created by Toni Brown
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Two equal powers of 2 merge. Two consecutive numbers in the Fibonacci sequence merge.
Created by Michael Darrow
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n + n = 2n, n + 2n = 3n, 2n + 3n = 5n. This is approximated using 12-tone temperament. At higher numbers, close enough numbers may end up acting as the same tile.
Created by Michael Darrow
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n + n = 2n, n + 2n = 3n, 2n + 3n = 5n. This is approximated using 15-tone temperament. At higher numbers, close enough numbers may end up acting as the same tile.
Created by Toni Brown
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n + n = 2n, n + 2n = 3n, 2n + 3n = 5n, 2n + 5n = 7n, 4n + 7n = 11n. This is approximated using 22-tone temperament. At higher numbers, close enough numbers may end up acting as the same tile.
Created by Michael Darrow
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n + n + n = 3n, n + n + 3n = 5n, n + 3n + 3n = 7n, n + n + 5n = 7n. This is approximated using the Bohlen-Pierce scale, which is a 13-tone 3:1 temperament. At higher numbers, close enough numbers may end up acting as the same tile.
Created by Michael Darrow
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Merges occur between three equal tiles that are a power of 14, between a tile that's a power of 14 and two tiles that are triple that power of 14, or between two equal tiles that are seven times a power of 14.
Created by aren12345
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A mode similar to 1535 1536 1537, but with 2584-like merges instead of 2048-like merges.
Created by MathCookie
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1 is the 1st tile. The 1st, 3rd, 5th, 7th, and so on tiles merge with an equal tile. The 2nd, 6th, 10th, 14th, and so on tiles merge with the previous tile. The 4th, 12th, 20th, 28th, and so on tiles merge with the tile two tiles before it. In general, if a tile's index is a multiple of 2^n but not of 2^(n + 1), then it merges with the tile n tiles before it.
Created by MathCookie
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Similar to 3024. If a tile's index is a multiple of 2^n but not of 2^(n + 1), then it merges with the tile (2^n) - 1 tiles before it.
Created by Michael Darrow
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Two 1s merge into a 2. Two equal tiles merge with a tile that is twice them.
Created by Michael Darrow
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Two equal tiles that are one, three, or nine times a power of eighteen can merge. A tile that is one or three times a power of eighteen can merge with a tile that is double it.
Created by Michael Darrow
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Two equal tiles that are equal to one, negative one, two, or negative two times a power of three can merge. A tile that is four times or negative four times a power of three merges with a tile that is negative one-fourth of it.
Created by Michael Darrow
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A variant of 3125 that applies the "1 with every merge" change like 2047, 2186, and 2583 do for their respective modes.
Created by aren12345
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Tiles merge if they are in consecutive levels and have different colors, sort of like Bicolor 2584, keeping the color of the larger one. However, multiples of 3 count as both colors.
Created by Michael Darrow
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A positive or negative power of the square root of two can merge with a tile that is itself times positive or negative sqrt(2)-1.
Created by Michael Darrow
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Like 1535 1536 1537, but with four tiles per layer instead of three. Three different tiles from the same layer can merge into one tile of the next layer.
Created by Michael Darrow
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Two 1s merge into a 2. A tile that is a power of 2 merges with a tile that is double or triple itself.
Created by Michael Darrow
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Two 1s can merge. Larger tiles merge with the largest odd tile under them.
Created by Michael Darrow
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Two 1s can merge. Tiles merge with the largest tile less than them that is 1 modulo 3.
Created by Michael Darrow
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Three equal tiles can merge if they are a power of 45. A tile that's a power of 45, triple a power of 45, or nine times a power of 45 can merge with a tile equal to itself and a tile triple itself. A tile that's a power of 45 or triple a power of 45 can merge with a tile triple itself and a tile quintuple itself.
Created by MathCookie
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Quadronacci is a sequence Q_n that satisfies Q_n=Q_(n-1)+Q_(n-2)+Q_(n-3)+Q_(n-4). A Q_n and a Q_(n-1) can merge (n can be any number),A (Q_n+Q_(n-1)) and a (Q_(n-2)+Q_(n-3)) can merge. Q_1~Q_4 are all 1.
Created by aren12345
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Two 1s can merge into a 2, and a 1 and a 2 can merge into a 3. Merges occur between a tile that's three times a power of three and a tile that's one, two, or three times that power of three, or between a tile that's four times a power of three and a tile that's five times that power of three.
Created by Michael Darrow
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You found Vilgeron's secret lair, evaded the traps, and are now ready to fight Vilgeron themself. Can you defeat Vilgeron or will Vilgeron defeat you first?
Created by Michael Darrow
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2378, but it starts with 1+1+1=3 instead of 1+1=2.
Created by Michael Darrow
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1000, except 5n+5n merges include a 1 as a third tile.
Created by Michael Darrow
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2s and 4s are the first tier of tile. Merges occur between two equal tiles and one of the other tile on the same tier.
Created by Toni Brown
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This mode uses the F_-1 = 0 convention for Fibonacci numbers. Merges may occur between two equal 2^n * F_n tiles, or between a 2^(n+1) * F_n tile and two 2^n * F_(n-1) tiles.
Created by Michael Darrow
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Any two 5-smooth tiles may merge if their result is also 5-smooth. This is approximated using 22-tone temperament. At higher numbers, close enough numbers may end up acting as the same tile.
Created by Toni Brown
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A tile that is divisible by 2^2^n - 1 but not by 2^2^(n + 1) - 1 merges with two tiles that are a (2^2^n - 1)th of it.
Created by Michael Darrow
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Merges occur between three equal throdd tiles, or between two equal throdd tiles and a threeven tile that is one away from them.
Created by Michael Darrow
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Three 1s can merge into a 3, and three 3s can merge into a 9. A merge occurs between a tile that's a power of three, a tile that's triple that power of three, and a tile that's nine times that power of three, or between a tile that's a power of three and two tiles that are thirteen times that power of three.
Suggested by Michael Darrow, created by MathCookie
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Three 1s merge into a 3. Two unequal tiles that are one away from the same power of two can merge with a 1 or -1.
Created by Michael Darrow
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The tiles in this mode come in RGB colors. Two tiles of the same tier that are different primary colors can merge. A secondary color tile can merge with its complementary color tile of the same tier. A white tile can merge with any primary color tile of its tier, creating that primary color tile of the next tier.
Created by MathCookie
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Merges occur between three equal tiles that are a power of 16, between two or three tiles that are triple a power of 16, between a tile that's a power of 16 and a tile that's nine times that power of 16, or between a tile that's six times a power of 16 and a tile that's ten times that power of 16.
Created by marouane
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Two equal tiles can merge if they are a power of 2 or if they are of the form (2n+1)*2^k, where k is 2n-1 or 2n. A (2n-1)*2^(2n-1) tile can merge with a 2^2n tile.
Created by aren12345
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3120, but the equal-tile merge is at the start of each tier instead of the end of each tier.
Created by Toni Brown
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Two 1s merge into a 2. 1 and 2 are considered the first "tier" of tiles. A tile on tier n merges with a tile whose difference with it is 2^(n - 1).
Created by MathCookie
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All of these, plus some other Custom Modes that aren't as good, were posted on my Discord server originally. If you made a Custom Mode and want to see it on this list, post it there or email me at mathcookie17@gmail.com.
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