Would be part of a cycle.

Seems very expensive, though I suppose it double-triggers landfall.

It seems plenty strong enough to me. Blue doesn't normally get any mana acceleration at all, and effects on lands are very useful because you don't use up a card playing them.

Absolutely. This is a very strong card.

But 99% of decks would just rather run an island. .. ah wait, I misread it. It doesn't replace itself with an island, you get an island as well. DOH.

Yeah, ok. competitive with the various artifacts if you're in monocolour.

Ah, right. Sorry. Yes, replacing itself with an island would indeed be nearly useless. (You could also imagine a card somewhere between, which came into play tapped and tapped for blue, but for a cost could landcycle itself instead, a bit like how this looked and a bit like existing multilands)

So, is this too good? Particularly since it can pay for its own cost?

To prevent it paying for its own ability, you could reword it to read:
: Add to your mana pool.
, : Search your library for an Island card and put it onto the battlefield tapped. Use this ability only if Alluvial Wash entered the battlefield this turn.

Alternatively, "As long as ~ is untapped", might make a cleaner card. Personally, I think the card is too strong, though. You've got to remember, that most cards that search through your library for a land set you back a card when you cast them. On Round three, you play this land and get something better than Kodama's Reach in mono-blue, since it put both lands directly onto the battlefield without using a spell in the process. I would suggest, at the very least, raising the cost to , but suspect that it would only be fair at , when it is officially past the cost of Explosive Vegetation. It may seem sad that you're nerfing this card, but trust me... I would run 4x the nerfed version of this card in every mono-blue deck I played. The ability to turn one land into two lands, without wasting any slots in my deck is phenominal.

It's not actually a Kodama's Reach / Exploding Vegetables. It's two lands, yes, but the card itself is one of them; it's only digging out one land. It's more like Farseeker Elf or Kor Cartographer. Or on the "land that gives you two mana" front, it's like Izzet Boilerworks and friends.

Given that green gets this ability more than other colours, I think the Cartographer's cost is about what nongreen should pay. So I think requiring is okay, if it's from other lands. Which means either , or and ETBT.

If this were ever used in a set, there would be a version for each color. Would the green version be allowed to be cheaper?

You're right, that's a much fairer cost, but now it's not that attractive, because once you're at five mana, accelerating further is more niche. It's hard to get a balance.

Yeah, you're right, it needs to see play to see when it's fun, and then be costed for that niche.