The original note, as written at the time
You want to have a green but well sheltered space. Here is how to do it. You divide the roof structure into a number of equal cells. You mount a set of roof covering elements on rails so that they are movable from cell to cell. The roof covering elements are cycled from cell to cell on a daily basis to ensure that the greenery below them always gets a fair share of sun regularly. This process can even be automated.
Ongoing development
A green but well-sheltered space, made by dividing the roof structure into equal cells and mounting the roof covering elements on rails, so they can be moved from cell to cell — cycled daily, so the greenery below always gets a fair share of sun. It can be automated.
The problem being solved is real and it is usually solved badly. Plants under a solid roof get no light. Plants under no roof get scorched. The usual compromise is a pergola, which gives every plant the same inadequate amount of both.
A moving roof gives each cell a turn. Shade today, sun tomorrow, and the average is right for everything. In a climate with this much sun, a fair share of it is a genuine resource to be scheduled.
The engineering problem is the rails, and it is severe: a roof is where water goes, and a sliding joint is where water gets in. Any working version has lightweight panels, steep falls, and a continuous flashing detail that tolerates movement — which is a detail most roofers will get wrong once and then avoid forever.
The automation is the least interesting part and the most likely to be sold as the feature. A motor and a timer are cheap. What matters is whether the panels can be moved by one person with a pole when the motor fails, because it will.
The best version is not a green roof with a moving cover. It is a shading system with a garden under it, which is a different thing to design and a much easier thing to maintain.