School of Numeromancy

Quandrix mages are ingenious math magicians. They study patterns, fractals, and symmetries underneath reality to command power over the fundamental forces of nature.  They'll solve intricate puzzles while contemplating the metaphysical properties of the universe.  They ponder whether the sciences are a feat of ingenuity or merely a lens to observe nature's majesty.

Quandrix is filled with highly intellectual nature-mathematicians. The students of Quandrix wield their power from the fundamental mathematics of nature, studying fractals, patterns, and symmetries. Quandrix mage-students have the ability to summon creatures that are made up of fractals. They are also able to expand their knowledge and even their physical size through the manipulation and bending of numbers. Their college motto is 'Math is Magic'.  Their magic is formulaic, blending math into their spellcasting.

Fantastical Fractal

Beginning when you select this school at 2nd level, as an action you can summon a Fractal Mascot to aide you.  You can command it as a bonus action in battle.  As you increase in level this fractal becomes stronger.  At each level increase the mascots hit points by 15.  Starting at level 5 increase strength, constitution and dexterity by 1 to a maximum of 20.  

Exponential Growth

Starting at 6th level, you can as an action you can expend a spell slot to target anything you can see within 40 feet: 

• Increase or decrease target's size by x categories where x is the level of the spell slot minus 2.
• Increase to a maximum of 22 or decrease to a minimum of 6 one ability score of a target by y where y is the level of the spell slots minus 3.
• Increase or decrease a target's AC by z where z is the level of the spell slot minus 4.
• Restore or reduce the number of spells slots of a target by D where D is the level of the spell slot plus your proficiency bonus.  These can be in any combination, for instance if the spell slot plus proficiency bonus is 12 you can remove 5 first level slots and 1 seventh level slot. 
• You can increase or decrease the number of actions a target can take on their round by l where l is the level of the spell slot minus 5.   

All these effects last 1 minute.  If the target is an unwilling creature they must make an intelligence saving throw against your spell save DC.  Once you use this feature you cannot use it again until after a short rest.  

Microscopic Blackhole

At 10th level, you have mastery over shape and matter.  You can, as an action, create a microscopic black hole.  For up to 1d4 plus your proficiency bonus rounds you can move the black hole 30 feet in any direction, including through solid objects.  Anything that comes into contact with the black hole takes 4d8 force damage if they fail a dex save against your spell save DC.  After the maximum number of rounds have finished, or you spend a bonus action, the black hole evaporates instantly.  Each creature within a 20-foot-radius sphere centered on the point before evaporation must make a Dexterity saving throw. A creature takes 3d8 fire damage and 3d8 force damage on a failed save, or half as much damage on a successful one.

Topological Spell Casting

Starting at 14th level, you can use your action to enhance yourself whilst aiding an ally.  You can,

• Teleport anywhere you can see within 60 feet.
• You can reverse gravity in a cylinder 5 feet around you.
• You can use arcane recovery without using one of its charges.
• You can swap places with a willing ally who you can see within 30 feet.
• You can use your knowledge of fractals to give you 40 + 8 times half your wizard level temporary hit points.

You can use each feature twice per long rest.