Addon Idea: Knights of Calculus (?)
Posted: Wed Jun 26, 2013 8:58 am
I think that ToME needs and will always need more crazy classes, because that's basically what I play it for
. So, I thought about making a mathematical-themed addon (name is work in progress). This class should rely on changing battlefield and enemies (unique feature ftw!) and good old melee combat.
Main stats are Str, Wil, Cun. Resurces are Stamina and Focus.
Focus dynamics: Focus attracts to 20% of maximum, just like Pos/Neg energy. If above 50%, every turn there is a chance that some talents won't decrease their cooldowns (you are so focused on doing math that you are half-stunned). Low-level talents (1, 2, 3 on unlocked trees, none or 1 on 10+ trees) increase Focus, higher-level consume vast amount of it, so, you'll need to suffer half-stun to actually cast them. Focus scales with Wil (boring, I know).
Heres my thoughts on talent trees:
Dirty Fighting 1.1 - not sure if locked or not. This class should benefit from it due to Cun being generally useful, but is it Knight-y?
Combat Tech 1.1 - definitely, and definitely unlocked, because melee is hard without it. (If you think otherwise, tell me).
Calculus Combat/Limits (1.3, Cun):
level 1: Unbound Sequence: for every given number, you'll have a greater one for some point in future!
Gain (50-250, talent lvl)% global speed bonus and continue to attack for 3 turns or until first miss with increasing base power. Every critical you land extends the duration of effect for 1 turn. You will instantly follow your opponent if it runs staying within your sight/infravision range, but the effect will break if it vanishes from your sight, including invisibility or hiding in plain sight.
level 2: Uniform Convergence: an uniformly convergent series converges to nearby numbers in nearby points.
All weapon damage you do within (6-10) turns is divided in equal parts and dealt over time, no more than (50%-100%, talent lvl) base weapon damage per turn; any weapon damage dealt to the same enemy while this effect is in action is postponed until it ends. When all damage is dealt and nothing is postponed anymore, enemy also receives extra damage, ignoring resistances, for 3 turns, each turn damage is (20-80%, scales with Str) of last turn's, first turn's is based on last damage done with aforementioned effect. (Whew, this sounds compilcated, isn't it? Basically, all damage you do is smeared over time, and receives additional "echo" effect for bonus damage. Numbers are subject for tweaking and a point for feedback!)
level 3: Conditional Convergence: by switching places of terms, you can greatly change the outcome!
Activated, gives you (500%-1000%, scales with talent lvl and maybe Dex?) speed, Free Action and ability to shuffle with critter or normal enemies - for 1 game turn (I'll try and make sure to make it full turn). If you do something that is not shuffling, this effect ends. Has 20ish cooldown.
level 4: Radius of Convergence: a series has a limit inside a disk, and bad outside of it.
Pins all creatures in radius 3-6, and increases your damage against them. This effect ends after 5 turns or when you leave the disk yourself. As long as you stay in center, it will also pin any new creatures coming into radius.
Calculus Combat/Infinitesimal (1.3, locked, 10+, Cun):
level 1: Differentiation: a derivative represents a relation between change of an argument and an outcome.
Hit a nearby foe for 100% weapon damage; if an attack lands, it will lose 10n % of its current life and all other resources, and n clones with 10% of its life and all other resources will emerge nearby. They will be sided with him, permanent, and will continue to exist after his death, so beware!
level 2: Integration: integration is adding infinite amount of zeros together.
Place an aura on a creature (including yourself) for 5-9 turns. It will absorb all damage done, predating shields, resistances and other special effects, and after an effect ends, inflict 10% of absorbed damage, bypassing damage shields and resistances.
level 3: Fundamental Theorem: there seems to be some connection between tangents and areas!
Sustain for max Focus: all weapons have Mind burst on hit, including when using weapons in special abilities; all non-melee abilites have their range increased by 1.
level 4: Mathematical Model: "How can it be that mathematics <...> is so admirably appropriate to the objects of reality?"
For simplicity, you assume that target creature is dumb and simple for 5 turns; your ability to correctly predict its behaviour under such heavy assumptions confuses every creature in a radius 2-4 of target for around 3 turns. The power and duration of confusion scales with your Willpower.
Math/Set theory (1.1, Wil): sets are building blocks for mathematical universe.
level 1: Finite Set: a finite set can be defined by enumerating its elements.
Damage all seen creatures of certain general type for 50-150 Mind damage, scales with Wil.
level 2:Countable Set: a set which elements can be counted using natural numbers.
Project an infinite-(or 15-?)range beam, slightly damaging all creatures in its way and bringing them as close to you as possible along the beam.
level 3: Diagonal proof: there are sets that are beyond being countable.
Sustain for max Focus: you convert all Mind damage you do to a type of damage that the foe has the least resistance for (except for physical), thus providing a counter-example. Your attacks may also trigger special effects based on damage type.
level 4: von Neumann universe: numbers are sets of sets of empty sets; they mean nothing to you.
For next X turns, you may ignore a hit if it would take more than 10% of your max life. After Y ignored hits, this effect ends.
Math/Topology (1.1, Wil): a study of shapes and spaces. [Probably generic talent tree]
level 1: Compact space: I cannot think of witty description here.
You surround yourself with a compact space of radius 3, which repels incoming projectiles and damages all creatures crossing its borders. For each projectile or creature crossing a border, the duration of this effect is lowered by one.
level 2: Haussdorf space: distinct points have disjoint neighbourhoods..
Each creature attacking you in melee combat (attacking and standing in melee range, to be precise) is knocked back for 3-5 tiles, suffering damage if it hits a wall or if it is immovable/knockback immune/pinned.
level 3: Homotopy: two objects are homotopic if there is continuous deformation of one into another.
Lower creature's life, increasing its level and ability levels. Cannot be casted on yourself.
level 4: Topological equivalence: many different real-life objects are actually very alike in topology.
Replaces a creature with abother one of the same level and type, assuming their topological equivalence. Rares, uniques and bosses are too special to be equivalent to something, and this ability will fail on them. This costs all of your Focus and then some
.
Math/Forbidden (1.1, Wil, locked 10+): in your quest for ultimate truth, you tap despised and forbidden hypothesa of mathematics. [Generic tree, too]
level 1: Continuum Hypothesis: you refuse it with your heart, allowing you to stare into unknown number of infinities between natural and real numbers.
This passive ability increases the threshold for Focus to half-stun you and reduces the cooldown of all Math talents by two and all Calculus Combat talents by 1. The threshold increase scales with Wil.
level 2: Parallel Postulate: exploring its alternatives allows you to slightly bend straight lines.
Targeting an empty space with beam or bolt Math or Calculus Combat ability will seek nearby foe in radius X and hit it instead. It will also allow Countable Set ability to draw single-standing creatures slightly off the line.
level 3: Axiom of Choice: as inconstructive as it may be, things that you can make with it drive you crazy.
Increases the number of Differentiation derivatives, and lets you switch places with any friendly target in radius X as if it is was standing near you.
level 4: Riemann Hypothesis: this insanely complex hypothesis is so beautiful and promising, you just don't want to wait for it to be proved.
The only non-passive ability in this tree. Upon activating it, you get a status effect for 14-10 turns that will cancel if you get hit (shield counts, too), attack, or use a talent. After this effect comes off naturally, you will get one-turn opportunity to do 2000% damage with your next attack or ability. This effect will also regenerate your Focus insanely fast, and after final blow, you will be left with exactly zero.
Calculus Combat/Complex Analysis (1.3, Cun): [Generic tree, definitely]
level 1: Entire function: any non-constant entire function on a complex plane is unbounded and has a root.
Teleport to a random point of radius X cone, no closer than Y.
level 2: Pole: a pole is well-behaved, isolated singularity.
Create a pole on the ground. Anything stepping on it will be violently knocked back in random available direction (one of
.
level 3: Removable singularity: it's merely cosmetic, and it's possible to redefine a function to remove it.
Render a tile impassable, for no good reason. If somebody is standing there, it will suffocate and won't be able to leave.
level 4: Essential singularity: it's not removable, and is not well-behaved.
Place an essential singularity, rendering tile impassable for all kinds of movement, with a chance to confuse, draw closer or knock back random target in range X each turn.
Only one singularity may exist simultaneously.
Combat training (1.3) and Survival (1.0), too; Survival possibly locked.
Thoughts, suggestions, corrections of my English?

Main stats are Str, Wil, Cun. Resurces are Stamina and Focus.
Focus dynamics: Focus attracts to 20% of maximum, just like Pos/Neg energy. If above 50%, every turn there is a chance that some talents won't decrease their cooldowns (you are so focused on doing math that you are half-stunned). Low-level talents (1, 2, 3 on unlocked trees, none or 1 on 10+ trees) increase Focus, higher-level consume vast amount of it, so, you'll need to suffer half-stun to actually cast them. Focus scales with Wil (boring, I know).
Heres my thoughts on talent trees:
Dirty Fighting 1.1 - not sure if locked or not. This class should benefit from it due to Cun being generally useful, but is it Knight-y?
Combat Tech 1.1 - definitely, and definitely unlocked, because melee is hard without it. (If you think otherwise, tell me).
Calculus Combat/Limits (1.3, Cun):
level 1: Unbound Sequence: for every given number, you'll have a greater one for some point in future!
Gain (50-250, talent lvl)% global speed bonus and continue to attack for 3 turns or until first miss with increasing base power. Every critical you land extends the duration of effect for 1 turn. You will instantly follow your opponent if it runs staying within your sight/infravision range, but the effect will break if it vanishes from your sight, including invisibility or hiding in plain sight.
level 2: Uniform Convergence: an uniformly convergent series converges to nearby numbers in nearby points.
All weapon damage you do within (6-10) turns is divided in equal parts and dealt over time, no more than (50%-100%, talent lvl) base weapon damage per turn; any weapon damage dealt to the same enemy while this effect is in action is postponed until it ends. When all damage is dealt and nothing is postponed anymore, enemy also receives extra damage, ignoring resistances, for 3 turns, each turn damage is (20-80%, scales with Str) of last turn's, first turn's is based on last damage done with aforementioned effect. (Whew, this sounds compilcated, isn't it? Basically, all damage you do is smeared over time, and receives additional "echo" effect for bonus damage. Numbers are subject for tweaking and a point for feedback!)
level 3: Conditional Convergence: by switching places of terms, you can greatly change the outcome!
Activated, gives you (500%-1000%, scales with talent lvl and maybe Dex?) speed, Free Action and ability to shuffle with critter or normal enemies - for 1 game turn (I'll try and make sure to make it full turn). If you do something that is not shuffling, this effect ends. Has 20ish cooldown.
level 4: Radius of Convergence: a series has a limit inside a disk, and bad outside of it.
Pins all creatures in radius 3-6, and increases your damage against them. This effect ends after 5 turns or when you leave the disk yourself. As long as you stay in center, it will also pin any new creatures coming into radius.
Calculus Combat/Infinitesimal (1.3, locked, 10+, Cun):
level 1: Differentiation: a derivative represents a relation between change of an argument and an outcome.
Hit a nearby foe for 100% weapon damage; if an attack lands, it will lose 10n % of its current life and all other resources, and n clones with 10% of its life and all other resources will emerge nearby. They will be sided with him, permanent, and will continue to exist after his death, so beware!
level 2: Integration: integration is adding infinite amount of zeros together.
Place an aura on a creature (including yourself) for 5-9 turns. It will absorb all damage done, predating shields, resistances and other special effects, and after an effect ends, inflict 10% of absorbed damage, bypassing damage shields and resistances.
level 3: Fundamental Theorem: there seems to be some connection between tangents and areas!
Sustain for max Focus: all weapons have Mind burst on hit, including when using weapons in special abilities; all non-melee abilites have their range increased by 1.
level 4: Mathematical Model: "How can it be that mathematics <...> is so admirably appropriate to the objects of reality?"
For simplicity, you assume that target creature is dumb and simple for 5 turns; your ability to correctly predict its behaviour under such heavy assumptions confuses every creature in a radius 2-4 of target for around 3 turns. The power and duration of confusion scales with your Willpower.
Math/Set theory (1.1, Wil): sets are building blocks for mathematical universe.
level 1: Finite Set: a finite set can be defined by enumerating its elements.
Damage all seen creatures of certain general type for 50-150 Mind damage, scales with Wil.
level 2:Countable Set: a set which elements can be counted using natural numbers.
Project an infinite-(or 15-?)range beam, slightly damaging all creatures in its way and bringing them as close to you as possible along the beam.
level 3: Diagonal proof: there are sets that are beyond being countable.
Sustain for max Focus: you convert all Mind damage you do to a type of damage that the foe has the least resistance for (except for physical), thus providing a counter-example. Your attacks may also trigger special effects based on damage type.
level 4: von Neumann universe: numbers are sets of sets of empty sets; they mean nothing to you.
For next X turns, you may ignore a hit if it would take more than 10% of your max life. After Y ignored hits, this effect ends.
Math/Topology (1.1, Wil): a study of shapes and spaces. [Probably generic talent tree]
level 1: Compact space: I cannot think of witty description here.
You surround yourself with a compact space of radius 3, which repels incoming projectiles and damages all creatures crossing its borders. For each projectile or creature crossing a border, the duration of this effect is lowered by one.
level 2: Haussdorf space: distinct points have disjoint neighbourhoods..
Each creature attacking you in melee combat (attacking and standing in melee range, to be precise) is knocked back for 3-5 tiles, suffering damage if it hits a wall or if it is immovable/knockback immune/pinned.
level 3: Homotopy: two objects are homotopic if there is continuous deformation of one into another.
Lower creature's life, increasing its level and ability levels. Cannot be casted on yourself.
level 4: Topological equivalence: many different real-life objects are actually very alike in topology.
Replaces a creature with abother one of the same level and type, assuming their topological equivalence. Rares, uniques and bosses are too special to be equivalent to something, and this ability will fail on them. This costs all of your Focus and then some

Math/Forbidden (1.1, Wil, locked 10+): in your quest for ultimate truth, you tap despised and forbidden hypothesa of mathematics. [Generic tree, too]
level 1: Continuum Hypothesis: you refuse it with your heart, allowing you to stare into unknown number of infinities between natural and real numbers.
This passive ability increases the threshold for Focus to half-stun you and reduces the cooldown of all Math talents by two and all Calculus Combat talents by 1. The threshold increase scales with Wil.
level 2: Parallel Postulate: exploring its alternatives allows you to slightly bend straight lines.
Targeting an empty space with beam or bolt Math or Calculus Combat ability will seek nearby foe in radius X and hit it instead. It will also allow Countable Set ability to draw single-standing creatures slightly off the line.
level 3: Axiom of Choice: as inconstructive as it may be, things that you can make with it drive you crazy.
Increases the number of Differentiation derivatives, and lets you switch places with any friendly target in radius X as if it is was standing near you.
level 4: Riemann Hypothesis: this insanely complex hypothesis is so beautiful and promising, you just don't want to wait for it to be proved.
The only non-passive ability in this tree. Upon activating it, you get a status effect for 14-10 turns that will cancel if you get hit (shield counts, too), attack, or use a talent. After this effect comes off naturally, you will get one-turn opportunity to do 2000% damage with your next attack or ability. This effect will also regenerate your Focus insanely fast, and after final blow, you will be left with exactly zero.
Calculus Combat/Complex Analysis (1.3, Cun): [Generic tree, definitely]
level 1: Entire function: any non-constant entire function on a complex plane is unbounded and has a root.
Teleport to a random point of radius X cone, no closer than Y.
level 2: Pole: a pole is well-behaved, isolated singularity.
Create a pole on the ground. Anything stepping on it will be violently knocked back in random available direction (one of

level 3: Removable singularity: it's merely cosmetic, and it's possible to redefine a function to remove it.
Render a tile impassable, for no good reason. If somebody is standing there, it will suffocate and won't be able to leave.
level 4: Essential singularity: it's not removable, and is not well-behaved.
Place an essential singularity, rendering tile impassable for all kinds of movement, with a chance to confuse, draw closer or knock back random target in range X each turn.
Only one singularity may exist simultaneously.
Combat training (1.3) and Survival (1.0), too; Survival possibly locked.
Thoughts, suggestions, corrections of my English?