Pokemon Alpha Sapphire Randomizer Nuzlocke is a concept I came up with along with The4thGenGamer when he did his X Randomizer Wonderlocke, and now it lives on JustPlayPokemon! Here are the Wonderlocke rules, then the Randomizer part is explained afterward:

Pokemon Wonderlocke Rules:
1. You must catch the first Pokémon you find in a new route. If you have it or a family member of its species, you CANNOT catch it. Failure to catch it results a loss in a new partner!
2. The newly caught Pokémon MUST be WONDER TRADED (no in-game trades allowed). If you happen to get the same Pokémon as the one you traded, you may keep it (Hard-Mode players must trade again). If the Pokémon is one you've already captured (whether it be the same exact Pokémon, or its family member), you must trade again (also known as "dupes clause".
3. All given Pokémon (like the starters, Lapras, and Torchic (for those during the event)) cannot be traded and are soul-bound.
4. (Like any other Nuzlocke challenge), when a Pokémon faints, you MUST release it. (EXCEPTION: You may put it in a "Dead" box to be able to go back any look at your previous members for a memorial service.)

What is the RANDOMIZER in ‘Randomizer Wonderlocke’?
Pretty much, for each wonder trade that we would make, we roll a six-sided dice. If we get 1-2, we wonder trade once and keep the Pokemon. 3-4, two trades, and 5-6, three trades. The number we get is the wonder trade that we keep. So if 3 is selected, we make 2 wonder trades and keep the final pokemon. Basically this randomizes which pokemon we get to keep via wonder trade. Still confused? Watch this video as 4GG explains! (: http://youtu.be/_lHOlcvQK9U less