The goal here was originally to preserve the Black Hack’s simplified spell slots while reducing the number of "INT test with disadvantage " during combat. Spell components here are a generic consumable like rations, trading cash for better spell retention. I got the idea for discovery of “wandering spells” from Hearthstone where the Mage is constantly drawing or discovering random spells. I thought it gave the feeling of conjuring up and channeling arcane powers well, and tying spells to particular locations gives Wizards more reason to go out and explore - spells becoming a kind of ambient treasure, invisible to other classes but fascinating to Magic Users, and another way to convey the themes and atmosphere of the location.
Arcane Magic
On every odd level the Wizard gains a single spell slot of one level higher than his previous slot - so a level 5 wizard memorizes one spell each of levels 3, 2, 1. A spell slot can be used to memorize lower level spells but this will seriously impact the Wizard’s total number of castings per day.
A Wizard also gains bonus slots for Intelligence - a level 1 slot at 13, a level 2 slot at 16, and a level 3 slot at 18.
When the wizard casts a spell, make a retention roll using 1d6 on the following table, adding 1 to the roll if the spell being cast is level 1, and adding another 1 if spell components were used:
1 - Oblivion: The spell is forgotten entirely.
2-4 - Entropy: The spell is replaced by a random spell from the Wizard’s book, one level lower.
5 - Equilibrium: The spell is replaced by a random spell from the Wizard’s book, of the same level.
6 - Inspiration: The spell is replaced by an unknown spell, determined by the DM.
7 - Endurance: The spell remains memorised.
8 - Epiphany: Roll again with no modifiers, and also gain a random spell per Inspiration.
Spells gained through Inspiration cannot be written down - the wizard doesn’t fully understand them - but are significantly easier to subsequently research.
Inspiration spells can be drawn from a master list of spells for the campaign or rulebook, but locations can also have their own lists - “wandering spell” tables for particular dungeons. So exotic locales might provide opportunities for learning strange magics, Necromancers would haunt dank crypts to perfect their art, hydromancers would dwell in sea caves and so on.
Certain high-magic or low-magic areas might similarly give a standing bonus or penalty to the roll - a magical wasteland might rapidly fatigue a mage, while a legendary font of magical energy could provide a nearly inexhaustible reservoir of spells.