Island Generator

I fully agree.

As a more general strategy, just use integers (preferably unsigned integers) for all critical stuff such as state handling and looping over. Then, perform floating point operations only on top of that, as a last step. Sometime you don't even need that and use fixed point arithmetics instead (i.e. change your unit to some fixed fraction, e.g. in accounting calculate with integer cents instead of floating point euros/dollars).

We can do better. It's true that decimal representation doesn't work:

    0.999999 = 0.142857 + 0.142857 + 0.142857 + 0.142857 + 0.142857 + 0.142857 + 0.142857 

And yes, rewriting the problem in an integer-indexed form does get the correct result:

    1 = (1 + 1 + 1 + 1 + 1 + 1 + 1) / 7

But what we want, in both the original code and in this example, is to calculate:

        1   1   1   1   1   1   1
    1 = — + — + — + — + — + — + —
        7   7   7   7   7   7   7

That's even hard to type out in our limited format here on HN. But it's what we mean to do.

Maybe better tooling could infer that if the limited math produces an angle indistinguishably close to 2pi, we probably meant for it to be equal to 2pi. Maybe it could do fractional addition, instead of converting to a decimal representation and truncating the number of digits.

Maybe it would write the outputs of the function in the initial triangle example, instead of as

    ([50 0]
     [-24.99999999999999 43.30127018922194]
     [-25.00000000000002 -43.301270189221924])

it would be represented as

    ([50 0]
     [-25 25*sqrt(3)]
     [-25 -25*sqrt(3)])

Because the sine of 2pi/3 is sqrt(3)/2, not 0.866.

This is a good reference, thanks.

Thanks for the Musgrave reference, I'll check it out.

As far as your geological questions:

1) Silted up seas and canyon-filled mountains aren't actually that inaccurate. Mountains as we think of them are highly eroded, basically just the remnants of much larger volumes of rock that were uplifted. I'd ballpark a 'typical' mountain range (Rocky Mountain front range, Appalachians, Alps, NZ Southern Alps) at having 10-20% of the uplifted volume of rock remaining. Say the mean elevation of a mountain range is 1 km above the surrounding land, the peaks may be ~2 km above. The rocks that make up those peaks (granite, gneiss, schist) might easily have formed at 10 km depth, so ~9 km of rock was removed through erosion.

Note most of this erosion happens during rock uplift, not after! So it's not like the mountains were super high and then got whittled down. I mean that happens but it's less dramatic than you may think. So the 'stream first' approach is not wrong--the two processes are simultaneous.

2) Ocean basins are huge, and very deep, but there are very large accumulations of sediments there. The oceans are so deep not simply because the crust is thinner, but because it's more dense. Tectonic plates are basically rafts of rock floating on a more dense mantle, and ocean plates are ~10% more dense than continental plates, so they sit lower (Archimedes' principle). However there giant 'fans' of sediment where big rivers, especially those draining actively rising mountains, hit the sea. The Bengal fan, where the Ganges empties into the Indian ocean, is a good example. But the fans are tiny compared to the ocean basins.

In subuction zones, as you've mentioned, the sediment does get squeezed and thickened. Though the oceanic plate in a subduction zone may be 8 km below sea level, in some cases erosion of the plate, sedimentation in the 'trench' and tectonic thickening of the sediment may be enough that it fills the trench in completely and comes above sea level. Barbados is an example of this.

The sediments in subduction zones trenches (called 'accretionary prisms') do eventually get compacted and heated enough to become rock again and pasted onto the sides of the continent. Often after enough ocean plate is subducted, there will be some islands or microcontinents on the oceanic plate that are too thick and buoyant to get subducted and they will smash into the continent, and all the sediment in between becomes incorporated in between, and melted and metamorphosed enough to look a lot like the continents in between. This is how continents grow.

3) The causes of plate tectonics are very well understood--The mantle is convecting because it's much hotter near the core than at the surface. Oceanic plates are more or less the surface of those convection cells, and continents are light by-products that don't get subducted back around but get moved around and smashed into each other and pulled apart by the convection below.

There are also things called 'mantle plumes' that are less well understood but seem to be places at the core-mantle boundary that are much hotter and send up very localized batches of magma to the surface. These are small, relatively stationary, and independent of mantle convection, and so they basically perforate the plates as the plates slide by. Like a machine that spurts frosting onto cookies on a conveyor belt, except upside down. Or something. This is what Hawaii is.

4) I had a 4 but I'm cooking dinner and forgot what it was.

That should be 783 kb, right?