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Math and Mechanus VI: Sets as Monsters

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Living Sets are akin to living spells, but rather than being manifestations of magic they are manifestations of Law. As such, most living sets are either LE, LN, or LG and only in rare cases are they chaotic. Each living set has some assortment of magical abilities which it uses in its chosen mission. They cannot be seen save by spells such as true-seeing, which reveal an amobea like creature formed from light. Geometric crystals sparkle within its body, flickering with their own energies. Sets vary in color and size as well. The origin of living sets is unclear, some believe they arise from the plane of Mechanus, others suspect the hand of the mysterious Axioms. The beings may come from Mechanus, but they are found across the planes though they are incredibly rare to the point many believe members to be unique.

Wherever they come from, living sets are protectors. Each set seeks out a group that it considers its members to bond with, whether this a forest or a tribe of nomads. The set then grants some magical blessing or bonus to those within its boundary, or makes them difficult to locate so long as they remain in its body. Those seeking to enter at best experience miasma (even if set and members are willing), at worst they are attacked with death magic. The closer an "intruder" is to a "member", the less it feels any undirected effects.

The more powerful sets can simply exclude non-members with an effect similar to a wall of force. Any who wish to enter can attempt to exorcise the set, or attack it. Sets cannot be harmed by physical means, and are immune to all spells save those possessing the lawful or chaotic descriptor. They take double damage from chaotic spells, and half damage from lawful ones unless lawful beings are immune. Fooling the set with enchantments is possible only if one is fooled themselves, i.e. to convince the set you are a goblin you must enchant yourself to believe it. Shapechange can lessen the effect of undirected effects.

Once it has decided who its members are, sets are incredibly limited in their ability to change their members. Members can be added in accordance with the existing members. Any being that is expected to remain a member for its lifespan may become a member--thus members by birth and marriage are usually acceptable. This also works for removing membership for any reason that exclude a being from the group. LG beings may exclude murderers, while harsher LN groups may say divorce excludes a member. Exclusion means suffering the undirected effects of being a non-member, and crueler sets will use their spell-like abilities to drive this person off.

However sets do have the following abilities:

Not: A set that is betrayed by its members can invert its protective power so that now harmful effects are targeted on those it once trusted. Upon killing all its former members, a set now has limited power against anything similar to its original membership. A Not-Set that once protected gnomes can now use some of its power against other gnomes, though these other victims gain bonuses to saving throws. Betrayed by those it considered family, these sets often end up bitter and malignant. Not-Sets are far more likely to be chaotic. The change to Not-Set is permanent.

And: Two sets can allow their members to interact without penalty using the "And" power. And effects can be temporary, but it is up to the set to decide when to negate the effects. "And" is often used by sets found near each other, protecting groups at peace.

Union: Union joins two sets into one composite being, an action that is never taken lightly. Sets must have good reason to desire such a transformation. Sets that undertake a Union combine their powers, their HD, etc. If two groups of members build a city together, or migrating animals protected by one set enter the forest of another, the two may combine their powers. Using the Union power naturally increases the effect of their powers in accordance with their increase in HD.

Null: Beyond becoming a Not-Set, Sets can become Null-Sets if all their members are dead. As a set that has unwillingly lost its members is consumed by emptiness, they more often than not go mad and become Null-Sets. Null-Sets become living portals to the Plane of Vacuum, and can be seen without aid as dark blotches draining light and heat. Their madness creates a pall of physical and mental gloom around them.

Anyone engulfed by a Null-Set is affected as though by a cone of cold for every round they remain in its borders, and the victim cannot see or breathe unless they possess specific protections for travel in the Vacuum. For every round someone remains in the Null-Set, there is a 10% cumulative chance per round of being transported to the Elemental Plane of Vacuum, though this forceful transference can be negated by a will save. After ten rounds, the person must save every round they remain in the set or be transported. Null-Sets are driven to avenge their members, and their near immunity to most forms of attack make them dangerous foes.

As Void is Everywhere, Null-Sets can also planeshift at will. Upon gaining revenge, Null-Sets wander in a destructive-haze until they are put down by embarassed forces of Order. Only Null-Sets will attack other living sets.

Fixed Sets: Sets whose members are killed by someone else that choose not to become Null Sets are very lonely. However, they can still use their powers if they are protecting the remains of their members. These guardian sets are lonely enough that they may learn how to communicate with other beings and become sages in the field of abstract mathematics, which they have an intuitive grasp of. They can befriend new beings, but cannot accept new members. As such, all those entering their boundaries are still subject to some level of miasma though this doesn't usually have a rule based effect.

Subsets--Subsets are the offspring of living sets, who further specify a group of original members. A set protecting a city may create a subset to protect sailors who were born in the city when they travel. Subsets can be created twice per year, but are freewilled beings. These subsets may decide they have no wish to serve and wander off, or worse come to hate the members and become a Not-Set.

Inversion-- While Not-Sets are born of betrayal, inverted Sets are those who seek to make its members prisoners. Inverted sets bond with their members, but by doing so prevent them from leaving their area. Each member is allowed single Will Save to avoid this, afterward they are imprisoned within the boundaries of the set and cannot leave even in death. A Freedom Spell or Wish can free a single member. Inverted Sets are rare, as a set must come across a group that it wishes to imprision so strongly it is willing to forsake a more pleasant bonding. This is actually incredibly painful for the set and never done lightly. Inverted Sets are most likely all lawful, and those that have been encountered in recorded history have always been LN or LG and have chosen to secure great evils or chaotic beings.

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Re: Math and Mechanus VI: Sets as Monsters

As long as you're giving sets (outer planar) physicality, one neat trick would be to implement the Banach-Tarski paradox for real: one unit ball......two unit balls!

Some interesting premises.

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