Solar Mox0
Artifact T: Add one mana of any color that a non-artifact legendary permanent of you control could produce.
It's not legendary but it won't produce any mana unless you have a legendary permanent that it's not another mox (that's why I added non-artifact clause).
Unammed A
Land
~ enters the battlefield tapped unless you control an artifact. T: Add W or U.
Unammed B
Land - Plains Island
At the beginning of your end step, sacrifice this unless you control a white or a blue permanent.
Unammed C
Land - Plains Island
As long as you control a basic plains and a basic island, this produces C instead of any other type of mana.
Unammed D
Land - Paradise
When this enters the battlefield, if you control three or more paradises, choose two and sacrifice the rest. T: Add W or U.
Unammed E
Land
At the beginning of your upkeep, this deals 1 damage to you unless you control a white or a blue permanent. T: Add W or U.
Solar Mox is still a powerful Mox, it matches the color of any legendary land you play. Making it not legendary itself falls into to old way of Moxen, being able to drop them all and go to town with all that free mana.
A) Is quite good, I don't foresee any major issues with it. It encourages using 0-cost artifacts, but those are available to all decks anyways.
B) This cycle would massively favor aggressive decks, giving them fetchable mana with no downside.
C) I would argue that this constitutes an upgrade to the original dual lands. It's going to just be a dual land in most decks, they simply won't play basics of both types, and thus never have a risk of switching it's mode. But for decks that want colors early but want colorless later, this is a controllable means to switch your fetchable dual land into C mode. If this wasn't typed, and thus not fetchable, it might be OK.
D) This downside is unlikely to take effect in many games, making it simply a non-typed dual land. The downside is an interesting idea though, and I would explore the idea of Paradise lands that engage a downside if you have too many of them.
Perhaps: Idyllic Glade
Land - Paradise T: Add G or W. Activate this ability only if you control one or fewer Paradises. T: Add C. Activate this ability only if you control two or more Paradises.
?
E) Is a less extreme version of B. It still favors aggressive decks, but is still usable by other strategies.
There are a number of cards like Icy Manipulator or Mana Vapors that can lock down tapped lands. There have been a few times I used Icy to specifically hold down an opponents land banking on them being mana screwed for that color. To have that land deal 1 damage each time to that player is just icing on the cake.
Because of that, a better version of your example already exists as Ardarkar Wastes.
Uhm, yeah, F isn't something that would be printed.
Unammed G
Land
~ enters the battlefield tapped. T: Add W or U. If you control a legendary permanent, add one mana of any color instead.
I thought about using "control a creature" or "control an artifact", but it sounds just too good. Another idea that I had was gaining life, but a whole cycle of dual lands that gain life every time it's tapped it's just taking the refuge cycle to an extreme.
Edit. I'd say that G isn't printable either. The bonus of adding mana of any color is just too much for a whole cycle of duals. As another idea, I should replace it with:
Unammed GG
Land
~ enters the battlefield tapped. T: Add W or U. WU, T: Target creature gets something until end of turn.
The mana cost of the activated ability wouldn't be symmetric, each pair would have its own. Each pair would target a creature and grant two different abilities. Trample, flying, lifelink, first strike, haste, etc.
Artifact
T: Add one mana of any color that a non-artifact legendary permanent of you control could produce.
It's not legendary but it won't produce any mana unless you have a legendary permanent that it's not another mox (that's why I added non-artifact clause).
Unammed A
Land
~ enters the battlefield tapped unless you control an artifact.
T: Add W or U.
Unammed B
Land - Plains Island
At the beginning of your end step, sacrifice this unless you control a white or a blue permanent.
Unammed C
Land - Plains Island
As long as you control a basic plains and a basic island, this produces C instead of any other type of mana.
Unammed D
Land - Paradise
When this enters the battlefield, if you control three or more paradises, choose two and sacrifice the rest.
T: Add W or U.
Unammed E
Land
At the beginning of your upkeep, this deals 1 damage to you unless you control a white or a blue permanent.
T: Add W or U.
A) Is quite good, I don't foresee any major issues with it. It encourages using 0-cost artifacts, but those are available to all decks anyways.
B) This cycle would massively favor aggressive decks, giving them fetchable mana with no downside.
C) I would argue that this constitutes an upgrade to the original dual lands. It's going to just be a dual land in most decks, they simply won't play basics of both types, and thus never have a risk of switching it's mode. But for decks that want colors early but want colorless later, this is a controllable means to switch your fetchable dual land into C mode. If this wasn't typed, and thus not fetchable, it might be OK.
D) This downside is unlikely to take effect in many games, making it simply a non-typed dual land. The downside is an interesting idea though, and I would explore the idea of Paradise lands that engage a downside if you have too many of them.
Perhaps:
Idyllic Glade
Land - Paradise
T: Add G or W. Activate this ability only if you control one or fewer Paradises.
T: Add C. Activate this ability only if you control two or more Paradises.
?
E) Is a less extreme version of B. It still favors aggressive decks, but is still usable by other strategies.
Hidden Oasis
Land - Paradise
T: Add C.
T: Add W or U. Active this ability only if you control two or fewer paradises.
Unammed F
Land
At the beginning of your end step, if this is tapped, you lose 1 life.
T: Add C, W or U.
There are a number of cards like Icy Manipulator or Mana Vapors that can lock down tapped lands. There have been a few times I used Icy to specifically hold down an opponents land banking on them being mana screwed for that color. To have that land deal 1 damage each time to that player is just icing on the cake.
Because of that, a better version of your example already exists as Ardarkar Wastes.
Unammed G
Land
~ enters the battlefield tapped.
T: Add W or U. If you control a legendary permanent, add one mana of any color instead.
I thought about using "control a creature" or "control an artifact", but it sounds just too good. Another idea that I had was gaining life, but a whole cycle of dual lands that gain life every time it's tapped it's just taking the refuge cycle to an extreme.
Edit. I'd say that G isn't printable either. The bonus of adding mana of any color is just too much for a whole cycle of duals. As another idea, I should replace it with:
Unammed GG
Land
~ enters the battlefield tapped.
T: Add W or U.
WU, T: Target creature gets something until end of turn.
The mana cost of the activated ability wouldn't be symmetric, each pair would have its own. Each pair would target a creature and grant two different abilities. Trample, flying, lifelink, first strike, haste, etc.