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  The Geometer
  A
  cross all the worlds of Dungeons & Dragons,
  wizards exemplify the careful application of
  magic. Their scholarly approach to
  fundamentals of magic is typified by their
  keeping of a spellbook. Many wizards specialize
  in a particular field of magic, expressing
  themselves through a mastery of necromancy,
  illusion, war magic and more. But for some, specializing in
  the keeping of a spellbook has become an art and science in of
  itself.
  At 2nd level, a wizard gains the Arcane Tradition feature.
  The School of Geometry option is available to a wizard in
  addition to the options offered in the Player's Handbook and
  other supplements.
  School of Geometry
  As a member of the School of Geometry, you do not limit
  yourself to expertise within a single school of magic. Instead,
  you seek to understand and exploit the arcane connections
  which you can draw between different magical constructs.
  Followers of this tradition are sometimes known as
  geometers. Some practitioners are meticulous scientists,
  taking careful and precise measurements of the arcane aether.
  Others appear crazed or conspiratorial as they make hurried
  connections only they can understand.
  School of Geometry Features
  Wizard Level
  Features
  2nd
  Bonus Proficiency, Spell Map, 
  Arcane Topography
  6th
  Spell Link
  10th
  Off the Grid
  14th
  Geometer's Journey
  Bonus Proficiency
  When you choose this tradition at 2nd level, you gain
  proficiency in cartographer's tools.
  Spell Map
  Beginning at 2nd level, a geometer is able to understand their
  arcane power as a topographical map. The drawing of a spell
  map is part of the process a geometer must undertake when
  preparing their spells. When you have selected which spells
  you will prepare, draw a spell map according to the following
  rules:
  Draw a node representing each of your prepared spells and
  cantrips granted by your wizard class levels. Cantrips are
  treated as 0th level spells for the purposes of drawing your
  spell map.
  Draw straight-line connections between spells of the same
  spell level. The connections must form an unlooped chain
  with open ends, such that each spell is connected to two
  others of the same level, except for the ends of the chain
  which are connected to only one. For example, for four 1st
  level spells, connect the nodes as follows: o-o-o-o.
  Draw straight-line connections between each spell and all
  other spells of the same school (e.g. abjuration,
  necromancy) which are exactly one level higher or one
  level lower.
  Connections must not cross any other connections you
  have drawn.
  If you are unable to draw a straight-line connection which
  fits these rules, you may have to re-configure your pattern
  of nodes. If it is not possible to draw a potential connection
  under these rules, you cannot benefit from that connection.
  Some of your features are dependent on the closed loops
  and terminals you draw into your spell map. A closed loop is
  defined an area enclosed on all sides by spell connections
  which does not contain any connections. A terminal is defined
  as any spell which is linked to only one other spell.
  See the following pages for some example spell maps.
  Arcane Topography
  Starting at 2nd level, the layout of your spell map grants you
  insight into the fabric of reality. Its reservoirs reflect a well of
  power ready to spring forth at a moment's notice, and its
  rivers guide power to your fingertips.
  You gain a +1 bonus to your Initiative rolls for each closed
  loop in your spell map, and your wizard cantrips deal 1 extra
  point of damage for each terminal in your spell map. If a
  wizard cantrip affects more than one target, you may only
  apply bonus damage to one. The maximum for each of these
  bonuses is equal to 2 + half your wizard level (rounded down).
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  Sample Spell Map I: Miana Fenworth
  This spellmap contains the prepared spells and cantrips of a 4th level wizard with an Intelligence score of 18.
  It contains 4 closed loops and 1 terminal.
  Spell Link
  Starting at 6th level, the spells you link within the same
  reservoir can bleed into one another in a spectacular or subtle
  fashion. Whenever you cast a spell which is part of a closed
  loop in your spell map, you may choose one of the following
  effects to apply to that spell:
  If the spell deals damage, you may change the damage type
  to any other type dealt by a spell within the same closed
  loop.
  If the spell grants its target at saving throw, you may
  choose to change the type of saving throw to one required
  by another spell within the same closed loop. Given the
  unstable nature of spell links, you may only apply this
  benefit to a spell with a duration of 'instantaneous.'
  For example, if you cast a fireball spell linked to the same
  closed loop as phantasmal killer, you may choose to deal
  psychic damage instead of fire damage. Alternatively, you may
  switch the Dexterity saving throw required by fireball for a
  Wisdom saving throw instead, as required by phantasmal
  killer.
  You may use this feature a number of times equal to your
  Intelligence modifier (minimum 1). You regain expended uses
  when you finish a long rest.
  Off the Grid
  Starting at 10th level, the spells at the edges of your spell map
  bleed into the world around you. When you cast a spell of 1st
  level or higher positioned at a terminal in your spell map, you
  and all allies within 30 feet gain temporary hit points equal to
  the spell's level.
  Geometer's Journey
  Beginning at 14th level, the contours of your spell map can
  draw power from the aether. When you would expend a spell
  slot to cast a wizard spell of 1st level or higher, place a token
  over that spell's position on your spell map. If this spell is not
  connected to the last spell you covered with a token, or if it is
  already covered with a token, remove all the tokens from your
  spell map. Otherwise, if the number of tokens on your spell
  map is then equal to that spell's level plus one, you may
  choose not to expend a spell slot when you cast the spell. If
  you do, remove all the tokens from your spell map.
  You remove all tokens from your spell map when you finish
  a short rest or a long rest.
  Advice for Geometer Players
  Drawing a spell map can be time consuming,
  especially at high levels. A 20th level wizard with an
  Intelligence score of 20 has as many as 30 nodes to
  connect! In order to avoid leaving your fellow
  players waiting, consider coming to your game with
  a few spell maps already prepared. Adjusting a spell
  map is a significantly quicker process than drawing
  one from scratch if you only make a handful of a
  substitutions each day.
  A useful tool for building spell maps has been
  developed by /u/calpin99, available here.
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  Sample Spell Map II: Lady Fenworth, the Mindweaver
  This spellmap contains the prepared spells and cantrips of a 20th level wizard with an Intelligence score of 20.
  It contains 6 closed loops and 6 terminals.
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  Credits
  Design: Imogen Gingell 
  Illustration: Imogen Gingell 
   
  Typesetting with thanks to GM Binder
  (https://www.gmbinder.com)  
   
  Find more at The Dragon Above 
   
  (https://dragon-above.tumblr.com)
  Changelog
  v1.1 - 2019/03/06
  Arcane Topography: If a wizard cantrip affects more than
  one target, bonus damage now only applies to one.
  Spell Link: Saving throws can now only be changed for
  instantaneous spells.
  Geometer's Journey: Clarified that a given spell can only
  have one token at a time, and that you must expend a spell
  slot to place a token.
  Added proficiency in cartographer's tools at 2nd level.
  DUNGEONS & DRAGONS, D&D, Wizards of the Coast, Forgotten Realms, the dragon ampersand, Player’s Handbook,
  Monster Manual, Dungeon Master’s Guide, D&D Adventurers League, all other Wizards of the Coast product names, and
  their respective logos are trademarks of Wizards of the Coast in the USA and other countries. This material is protected
  under the copyright laws of the United States of America. Any reproduction or unauthorized use of the material or artwork
  contained herein is prohibited without the express written permission of Wizards of the Coast.  
   
  ©2018 Wizards of the Coast LLC, PO Box 707, Renton, WA 98057-0707, USA. Manufactured by Hasbro SA, Rue Emile-
  Boéchat 31, 2800 Delémont, CH. Represented by Hasbro Europe, 4 The Square, Stockley Park, Uxbridge, Middlesex, UB11
  1ET, UK.
  
SOURCE: textdata/thevault/Dungeons & Dragons [multi]/5th Edition (5e)/3rd Party/Imogen Gingell/School of Geometry (Arcane Tradition) v1.1.pdf