Divide By
The Divide By spells all have the same basic function - to copy the next spell after them in the wand. The specifics of the way this happens, and the interaction between them and other complex spells like Add Trigger and the Greek spells, make them some of the most powerful (and mind boggling) spells in the game.
Spells of any type can be copied, although copying Projectile spells is generally the most straightforward. Dividing Modifier spells is trickier. Limited use spells must have at least one charge remaining, and a charge will be consumed for each cast, but you can Divide a Greek spell like Gamma to indirectly copy without limit.
One Divide By can copy another - this is referred to as a Divide Chain. There are limits on how long these chains can be, with the largest possible number of copies from a chain maxing out at 800. See later on this page for working chains you can easily add to a wand.
The copying process imposes a Projectile Damage reduction, as well as reducing any previously-applied explosion radius bonus (e.g. from Explosive Projectile). All other damage types are unaffected, including Healing Damage - dividing Healing Bolt is very effective.
This page focuses on the most practical ways to use Divides - to gain a fuller understanding of how these spells work see: Expert Guide: Divide By Spells.
Unlocking
All the Divide By spells need to be unlocked before they will spawn in the world.
- The first 3 Divide By spells (2, 3, 4) are unlocked by opening the Coral Chest
- Divide By 10 is unlocked by bringing the Curse of Greed to the Avarice Diamond in The Tower.
Notes
- The virtual copies do not need extra free spell slots in the wand to function, so can be used to make even low capacity wands fire many more spells than normal.
- Divide By spells have a hidden effect of reducing the cast state explosion radius. The reduction is up to -5 for div2, -10 for div3, -20 for div4, and -40 for div10. This is capped at 0, setting the radius adjustment to 0 if the result is negative.
- All the Divide By spells set the cast state pattern angle to 5 (this is the same variable that the Formation multicast spells modify.)
- A pattern angle of 5 means that projectiles will be distributed at even intervals along a 10 degree arc centered where you're aiming.
- Only the last pattern angle to be set is used, and it is set after the spell setting it draws, so a Divide By drawing into a hexagon formation will have 5 pattern degrees instead of 180.
Useful Recipes
See the tables toward the bottom of this article for other numbers of copies.
Divide by 800 on a spell without draw (e.g. Projectile/Static Projectile spells)
This casts 800 copies of a Spark Bolt, which is the largest possible purely using Divides.
Divide by 800 on a spell with draw (e.g. Modifier spells)
This casts 800 copies of the Critical on Wet. In order to properly divide the modifier, the Divide By chain is draw canceled, which means that you need the additional draw from the Double Spell to cast anything after.
Divide by 800 add trigger (multiple Modifier spells)
These examples cast 801 copies of both Critical on Wet and Homing. The first build works because the Blood Magic is a utility spell without a related projectile, which causes the Add Trigger to fail (which is good since Add Trigger would normally ruin the deck for the next copy), but only after casting copies of the modifiers. In the second build, Add Trigger fails because it reaches the end of the wand with nothing to apply to. Add Timer and Add Expiration Trigger have the same behavior here. The Blood Magic can be replaced with Blood To Power, Gold To Power, or a projectile/static projectile with 0 charges (e.g. 0 charge Healing Bolt).
Divide by 800 spell duplication (Multiple Modifiers & Projectiles)
This gives 800 additional copies of Critical on Wet, Homing, and Spark Bolt. The Alpha calling Tau is used to hit the recursion limit, which prevents Spell Duplication from copying a Divide By or greek letter and ruining the deck before all 800 copies complete. It is also possible to use Gamma with Tau at end of the wand, with an additional double cast at the beginning, instead of using Alpha.
How it Works
All the example wands on this page have a link to the Wand Simulator site, which displays a casting sequence diagram that helps explain what Divide By is doing.
Here are the basics:
This works with modifiers and after triggers as well, so:
Is mechanically equal to:
Those multicasts are never actually created though, they're just there to illustrate behavior. In actuality, the original spell is deleted and new spells (with reduced damage output) are created in their place and cast at the same time.
When Divide By # is applied to a modifier, the spell works a bit more strangely.
This setup:
Becomes similar to this in the first cast:
The divide by effectively creates 2 additional copies of the Damage Plus. The first copy is prevented from drawing additional spells, but the second copy is able to draw into the real Damage Plus and Spark Bolt, which means you get a total of 3 Damage Pluses.
The next cast from that wand will be similar to:
This is because after the Divide By finishes copying the second Damage Plus (which drew the real damage plus and spark bolt), it will discard the next spell, which is the bouncing burst. The bubble spark gets cast with trigger, which then wraps.
It's the same for multicasts.
This:
Is equivalent to:
As in the previous example, the first Triple Scatter Spell is unable to draw, but the next two are. Which means that you get an effective 5 multicast, the same as 2 Triple Spells. The spread from all three Triple Scatter Spells will be applied.
Each Divide By spell has an iteration limit. Divide By 2 has a limit of 4, Divide By 3 and 4 have a limit of 3, and Divide By 10 has a limit of 2. Once this iteration limit is exceeded any subsequently chained Divide By spells will act as if they are "Divide by 1", and will not increase the number of copies.
This:
Will cast 100 Spark Bolts as expected, since the first Divide By will cast the second Divide By 10 times.
But this:
Will still only cast 100 Sparks Bolts, since the third Divide By 10 exceeds the iteration limit of 2.
The iteration counter is shared for all Divide By spells so this:
Will cast 20 Spark Bolts, while this:
Will cast 200 spark bolts.
Remember how weird dividing Modifiers is? Well the iteration limit can be used to make it a lot less weird. By purposefully hitting the limit (and causing the final Divide to act as a 'Divide By 1') Modifiers can be divided without issue many hundereds of times.
This wand will produce a very disappointing 21 copies of Damage Plus.
Fix this by adding another Divide By 10, which exceeds its' iteration limit of 2, allowing us to get the full 100 copies.
Things becomes more complicated when Divide By spells are placed after a multicast.
In this example:
The multicast will draw these four blocks, in order:
Notice how the second casting block begins with the spells following the first block, but is followed by the Divide By's and Spark Bolt. Each following block wraps into the same chain, except one spell further on the chain of Divide By's. A chain of n divide by spells needs a n+1 multicast in order to cast all possible blocks. Each of these blocks will have its own iteration counter.
Divide By Chains
One Divide By can copy another, but there are limits. Each Divide By has an iteration limit, which determines what positions it can occupy in a chain while still producing extra copies. Divide By 10 has a limit of 2, meaning it will only work if in the first two positions. Divide By 3 and 4 both have a limit of 3, and Divide By 2 has a limit of 4.
1st | 2nd | 3rd | 4th | 5th + |
---|---|---|---|---|
1st | 2nd | 3rd | 4th | 5th + | |
---|---|---|---|---|---|
- | - | Yes | Yes | Yes | |
- | - | - | Yes | Yes | |
- | - | - | Yes | Yes | |
- | - | - | - | Yes |
1st | 2nd | 3rd | 4th | 5th + | |
---|---|---|---|---|---|
× 10 | × 10 | × 1 | × 1 | × 1 | |
× 4 | × 4 | × 4 | × 1 | × 1 | |
× 3 | × 3 | × 3 | × 1 | × 1 | |
× 2 | × 2 | × 2 | × 2 | × 1 |
Divides placed after their limit don't produce any extra copies, but they do produce one copy - they can be considered to be a "Divide By 1". This is very useful since the first copy made by any Divide is prevented from drawing any additional spells from the wand. In particular, this makes it possible to copy Modifier type spells many times.
The second table above shows which Divides can be used in position 3, 4 and 5 to make the prior chain work with Modifiers (and other spells that draw).
Chain | Length | Total Copies | Cast Delay | Recharge Time | Damage Penalty | Radius Penalty |
---|---|---|---|---|---|---|
1 | 10 | 80 | 20 | -37.5 | -40 | |
1 | 4 | 50 | 0 | -15 | -20 | |
1 | 3 | 35 | 0 | -10 | -10 | |
1 | 2 | 20 | 0 | -5 | -5 | |
2 | 100 | 80 | 20 | -412.5 | -440 | |
2 | 40 | 80 | 20 | -187.5 | -240 | |
2 | 30 | 80 | 20 | -137.5 | -140 | |
2 | 20 | 80 | 20 | -87.5 | -90 | |
2 | 40 | 50 | 0 | -165 | -180 | |
2 | 16 | 50 | 0 | -75 | -100 | |
2 | 12 | 50 | 0 | -55 | -60 | |
2 | 8 | 50 | 0 | -35 | -40 | |
2 | 30 | 35 | 0 | -122.5 | -130 | |
2 | 12 | 35 | 0 | -55 | -70 | |
2 | 9 | 35 | 0 | -40 | -40 | |
2 | 6 | 35 | 0 | -25 | -25 | |
2 | 20 | 20 | 0 | -80 | -85 | |
2 | 8 | 20 | 0 | -35 | -45 | |
2 | 6 | 20 | 0 | -25 | -25 | |
2 | 4 | 20 | 0 | -15 | -15 | |
3 | 400 | 80 | 20 | -1912.5 | -2440 | |
3 | 300 | 80 | 20 | -1412.5 | -1440 | |
3 | 200 | 80 | 20 | -912.5 | -940 | |
3 | 160 | 80 | 20 | -787.5 | -1040 | |
3 | 120 | 80 | 20 | -587.5 | -640 | |
3 | 80 | 80 | 20 | -387.5 | -440 | |
3 | 120 | 80 | 20 | -587.5 | -740 | |
3 | 90 | 80 | 20 | -437.5 | -440 | |
3 | 60 | 80 | 20 | -287.5 | -290 | |
3 | 80 | 80 | 20 | -387.5 | -490 | |
3 | 60 | 80 | 20 | -287.5 | -290 | |
3 | 40 | 80 | 20 | -187.5 | -190 | |
3 | 160 | 50 | 0 | -765 | -980 | |
3 | 120 | 50 | 0 | -565 | -580 | |
3 | 80 | 50 | 0 | -365 | -380 | |
3 | 64 | 50 | 0 | -315 | -420 | |
3 | 48 | 50 | 0 | -235 | -260 | |
3 | 32 | 50 | 0 | -155 | -180 | |
3 | 48 | 50 | 0 | -235 | -300 | |
3 | 36 | 50 | 0 | -175 | -180 | |
3 | 24 | 50 | 0 | -115 | -120 | |
3 | 32 | 50 | 0 | -155 | -200 | |
3 | 24 | 50 | 0 | -115 | -120 | |
3 | 16 | 50 | 0 | -75 | -80 | |
3 | 120 | 35 | 0 | -572.5 | -730 | |
3 | 90 | 35 | 0 | -422.5 | -430 | |
3 | 60 | 35 | 0 | -272.5 | -280 | |
3 | 48 | 35 | 0 | -235 | -310 | |
3 | 36 | 35 | 0 | -175 | -190 | |
3 | 24 | 35 | 0 | -115 | -130 | |
3 | 36 | 35 | 0 | -175 | -220 | |
3 | 27 | 35 | 0 | -130 | -130 | |
3 | 18 | 35 | 0 | -85 | -85 | |
3 | 24 | 35 | 0 | -115 | -145 | |
3 | 18 | 35 | 0 | -85 | -85 | |
3 | 12 | 35 | 0 | -55 | -55 | |
3 | 80 | 20 | 0 | -380 | -485 | |
3 | 60 | 20 | 0 | -280 | -285 | |
3 | 40 | 20 | 0 | -180 | -185 | |
3 | 32 | 20 | 0 | -155 | -205 | |
3 | 24 | 20 | 0 | -115 | -125 | |
3 | 16 | 20 | 0 | -75 | -85 | |
3 | 24 | 20 | 0 | -115 | -145 | |
3 | 18 | 20 | 0 | -85 | -85 | |
3 | 12 | 20 | 0 | -55 | -55 | |
3 | 16 | 20 | 0 | -75 | -95 | |
3 | 12 | 20 | 0 | -55 | -55 | |
3 | 8 | 20 | 0 | -35 | -35 | |
4 | 800 | 80 | 20 | -3912.5 | -4440 | |
4 | 600 | 80 | 20 | -2912.5 | -2940 | |
4 | 400 | 80 | 20 | -1912.5 | -1940 | |
4 | 320 | 80 | 20 | -1587.5 | -1840 | |
4 | 240 | 80 | 20 | -1187.5 | -1240 | |
4 | 160 | 80 | 20 | -787.5 | -840 | |
4 | 240 | 80 | 20 | -1187.5 | -1340 | |
4 | 180 | 80 | 20 | -887.5 | -890 | |
4 | 120 | 80 | 20 | -587.5 | -590 | |
4 | 160 | 80 | 20 | -787.5 | -890 | |
4 | 120 | 80 | 20 | -587.5 | -590 | |
4 | 80 | 80 | 20 | -387.5 | -390 | |
4 | 320 | 50 | 0 | -1565 | -1780 | |
4 | 240 | 50 | 0 | -1165 | -1180 | |
4 | 160 | 50 | 0 | -765 | -780 | |
4 | 128 | 50 | 0 | -635 | -740 | |
4 | 96 | 50 | 0 | -475 | -500 | |
4 | 64 | 50 | 0 | -315 | -340 | |
4 | 96 | 50 | 0 | -475 | -540 | |
4 | 72 | 50 | 0 | -355 | -360 | |
4 | 48 | 50 | 0 | -235 | -240 | |
4 | 64 | 50 | 0 | -315 | -360 | |
4 | 48 | 50 | 0 | -235 | -240 | |
4 | 32 | 50 | 0 | -155 | -160 | |
4 | 240 | 35 | 0 | -1172.5 | -1330 | |
4 | 180 | 35 | 0 | -872.5 | -880 | |
4 | 120 | 35 | 0 | -572.5 | -580 | |
4 | 96 | 35 | 0 | -475 | -550 | |
4 | 72 | 35 | 0 | -355 | -370 | |
4 | 48 | 35 | 0 | -235 | -250 | |
4 | 72 | 35 | 0 | -355 | -400 | |
4 | 54 | 35 | 0 | -265 | -265 | |
4 | 36 | 35 | 0 | -175 | -175 | |
4 | 48 | 35 | 0 | -235 | -265 | |
4 | 36 | 35 | 0 | -175 | -175 | |
4 | 24 | 35 | 0 | -115 | -115 | |
4 | 160 | 20 | 0 | -780 | -885 | |
4 | 120 | 20 | 0 | -580 | -585 | |
4 | 80 | 20 | 0 | -380 | -385 | |
4 | 64 | 20 | 0 | -315 | -365 | |
4 | 48 | 20 | 0 | -235 | -245 | |
4 | 32 | 20 | 0 | -155 | -165 | |
4 | 48 | 20 | 0 | -235 | -265 | |
4 | 36 | 20 | 0 | -175 | -175 | |
4 | 24 | 20 | 0 | -115 | -115 | |
4 | 32 | 20 | 0 | -155 | -175 | |
4 | 24 | 20 | 0 | -115 | -115 | |
4 | 16 | 20 | 0 | -75 | -75 |
Gallery
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