Formation

This article is about the Formation group of Multicast Spells. For the terrain structures, see Heart formations and treasure locations.

Formation
Casts two spells: one ahead of and one behind the caster
Type	Multicast
Mana Drain	0
Pattern Arc	180
Spread Modifier	-5
Additional Information
ID	I_SHAPE
Spawning Behaviour
Spawn chance by Tier ⓘ	000 11/21010.48 21/27510.36 31/43310.23 400 500 600 700 800 900 1000
Casts 3 spells - ahead, above and below the caster
Type	Multicast
Mana Drain	3
Pattern Arc	90
Spread Modifier	-8
Additional Information
ID	T_SHAPE
Spawning Behaviour
Spawn chance by Tier ⓘ	000 11/21010.48 21/27510.36 31/32410.31 41/47610.21 500 600 700 800 900 1000
Casts 5 spells in a pentagonal pattern
Type	Multicast
Mana Drain	5
Pattern Arc	180
Spread Modifier	-12
Additional Information
ID	PENTAGRAM_SHAPE
Tags	multi
Spawning Behaviour
Spawn chance by Tier ⓘ	000 11/21010.48 21/34410.29 31/43310.23 41/71410.14 51/12520.10.08 600 700 800 900 1000
Casts 6 spells in a hexagonal pattern
Type	Multicast
Mana Drain	6
Pattern Arc	180
Spread Modifier	-15
Additional Information
ID	CIRCLE_SHAPE
Spawning Behaviour
Spawn chance by Tier ⓘ	000 11/84010.12 21/68810.15 31/43310.23 41/47610.21 51/41710.24 61/27310.37 700 800 900 1000
Casts 2 spells in a bifurcated pattern
Type	Multicast
Mana Drain	2
Pattern Arc	45
Spread Modifier	-8
Additional Information
ID	Y_SHAPE
Spawning Behaviour
Spawn chance by Tier ⓘ	01/55.621.80 11/16810.59 21/34410.29 31/43310.23 400 500 600 700 800 900 1000
Casts 3 spells in a trifurcated pattern
Type	Multicast
Mana Drain	3
Pattern Arc	90
Spread Modifier	-5
Additional Information
ID	W_SHAPE
Spawning Behaviour
Spawn chance by Tier ⓘ	000 100 21/34410.29 31/43310.23 41/28510.35 51/41710.24 61/27310.37 700 800 900 1000

Multicast Spells

The Formation spells are a set of multicast modifiers that distribute projectiles at evenly spaced intervals over an arc of fixed angle. Unlike the similar scatter multicasts that add a random spread angle to each projectile, the pattern created by a formation is exact and predictable.

Formation Angle

The Formation spells add multicast, and set the formation angle of the cast. The formation angle determines the total arc over which projectiles are spaced, with the exact spacing determined by the number of projectiles.

Working clockwise (starting from behind where you are aiming), each projectile appears in the same order as they are on the wand. Note: this does mean that the 'up' and 'down' projectiles vary based on the direction you are facing.

For example, with the 'Above and Below' variant, when facing to the East, the first projectile fires upwards, the second forward, and the third downward. If facing to the West, the first projectile fires downwards, the second forward, the last upwards.

List of Formations

The formation angles for each spell that sets one:

Spell		Multicast	Sets Angle	Formation Angle
	Behind Your Back	2	After Drawing	± 180°
	Pentagon	5	After Drawing
	Hexagon	6	After Drawing
	Iplicate	1	Before Drawing
	Quplicate	1	Before Drawing
	Peplicate	1	Before Drawing
	Heplicate	1	Before Drawing
	Above And Below	3	After Drawing	± 90°
	Tiplicate	1	Before Drawing
	Bifurcated	2	After Drawing	± 45°
	Yplicate	1	Before Drawing
	Trifurcated	3	After Drawing	± 40°
	Wuplicate	1	Before Drawing
	Freezing Gaze	0	When Cast	± 30°
	Divide By	0	After Copying	± 5°

Behind Your Back, Pentagon, and Hexagon all have the same 180 degree formation angle, differing only in the amount of multicast they have built-in.

• Using Pentagon or Hexagon to cast only two spells will have the same effect as using Behind Your Back.
• Combining Behind Your Back and Quadruple Spell has the same effect as Pentagon.
• Combining Behind Your Back and two Triple Spells has the same effect as Hexagon.
• For a Square formation, use Behind Your Back with Triple Spell.

Formation Angle - Calculation

To calculate the angle between all projectiles in a formation, the following formulae can be used.

For 360° formations:

$\color {Apricot}angle={\frac {formation\_angle}{projectile\_number}}$

For all others:

$\color {Apricot}angle={\frac {formation\_angle}{projectile\_number-1}}$

Combining Formations

Since it is always set to a fixed value by the spells that modify it, the formation angle for a cast is entirely determined by the last change made. The spell that changes it last depends on the evaluation order.

If multiple Formation spells are cast together, the last spell which completes its evaluation determines the formation angle for the entire cast. This is because the Formation multicasts draw first, and then set the angle afterward.

This is slightly different with the Plicate Spells, which copy, then set the angle, and then draw.

For more about spell evaluation, see Expert_Guide:_Draw#Spell_Evaluation.

Example 1:

#

In this case, Behind Your Back determines the formation since it draws Bifurcated (and thus Bifurcated completes its evaluation before Behind Your Back).

Shuffle

No

Spells/Cast

1

Tinker

However, in this case, Bifurcated determines the formation since Behind Your Back draws two spark bolts and therefore completes its evaluation.

Shuffle

No

Spells/Cast

1

Tinker

Example 2:

#

Let's bring all the concepts above together. Suppose we have the following wand:

Shuffle

No

Spells/Cast

1

Tinker

The wand fires as follows:

• Bifurcated draws Above And Below, so it finishes its evaluation last. The cast has a 90° formation angle.
• Above And Below does not change how the projectiles are fired. It simply acts as a multicast, identical to Triple Spell.
• The projectiles are now fired clockwise (starting from behind where you aim). Assuming you're aiming to the right, from top to bottom, you see:
  • Spark Bolt
  • Luminous Drill
  • Spitter Bolt
  • Firebomb
• The angle between all spells can be calculated from the formula above for non-360° formations:
  $\color {Apricot}angle={\frac {90^{\circ }}{4-1}}=30^{\circ }$

Bifurcation causes spells to fire within a 90° angle

Spells are ordered clockwise, starting from behind you

Example 3:

#

Here's an example using Behind Your Back instead.

Shuffle

No

Spells/Cast

1

Tinker

• Note that the first projectile (in this case, Spark Bolt) fires directly opposite from where you're aiming.
• The angle between the spells can be calculated from the formula above for 360° formations:
  $\color {Apricot}angle={\frac {360^{\circ }}{3}}=120^{\circ }$

Other formation spells

Some other spells modify the Formation Angle of a cast:

• Freezing Gaze - which sets it to 30 degrees
• The Divide By spells, which set it to 5 degrees
• The Plicate Spells, which set it to the same set of values

Typically the Formation multicast modifier will appear first, and so override these.

Tips

• Can be used to create patterns maximizing the area of arcing modifiers such as Electric Arc or a splash explosion-like effect when used with a Trigger.
• The order of the projectiles in the wand matters - they will be distributed, clockwise, across the formation arc in the same order they are executed.
• Spells that normally fire multiple projectiles, like Triplicate Bolt, can use multiple firing angles at once if an insufficient amount of other projectile spells are included with the multicast.
• Will apply to Always Cast spells on wands.
• Formation angle is referred to as pattern_degrees in the game's lua scripts.

See Also

• Tuple Spell
• Tuple Scatter Spell

History

• Apr 8 2024:
  • Formation - Behind Your Back
    • Base price reduced from 80 to 30 .
    • Spread modifier changed from 0 to -5.
    • Removed tier 4 spawning.
    • Changed spawn probabilities on tier 2 from 0.4 to 0.5, and tier 3 from 0.4 to 0.3.
  • Formation - Bifurcated
    • Base price reduced from 100 to 30 .
    • Spread modifier changed from 0 to -8.
    • Removed tier 4 spawning.
    • Changed spawn probabilities on tier 2 from 0.4 to 0.5, and tier 3 from 0.4 to 0.3.
  • Formation - Above and Below
    • Base price reduced from 120 to 30 .
    • Spread modifier changed from 0 to -8.
    • Removed tier 5 spawning.
    • Changed spawn probabilities on tier 2 from 0.4 to 0.5, and tier 4 from 0.4 to 0.3.
  • Formation - Trifurcated
    • Base price reduced from 160 to 50 .
    • Spread modifier changed from 0 to -5.
    • Changed spawn probability on tier 4 from 0.3 to 0.5.
  • Formation - Hexagon
    • Base price reduced from 150 to 50 .
    • Spread modifier changed from 0 to -15.
  • Formation - Pentagon
    • Base price reduced from 150 to 50 .
    • Spread modifier changed from 0 to -12.