Scientific simulations / scientific computing in Bevy

[alice-i-cecile]

Bevy has tremendous potential as a framework for scientific simulations: it's fast, modular, easy to read/write and hooks in readily to convenient features like graphics and UIs.

This is a tracking issue to discuss the important features to help us get there (h/t @alec-deason). Many of these are "ecosystem" issues, rather than something that needs to be solved by the Bevy engine itself.

Universal features

1. Improved documentation and API maturity. Templates and guides are a big part of this, as is battle-tested correctness.
2. Charts / graphing integration.
3. Statistical integrations.
4. Ergonomic data logging.
5. Headless mode (Headless rendering to images #22, bevy cli #436), with good file-driven configuration.
6. Deterministic RNG. This includes good enough APIs to get to zero-system ambiguities (Ambiguous system ordering #1312) and ordered query iteration (Ordered iteration over Queries #1470), but the story is complex.
7. Fixed point support, for more stable computations.
8. Ergonomic saving and loading (First class save / load support #1442) with checkpointing.
9. Cross-machine distributed processing.
10. System order visualization and modification.
11. Better testing and correctness tools. Archetype Invariants #1481 is a good start.

Domain specific features

1. Indexes (Prototype Indexing #1587, Allow entities to store multiple components with the same type #1527), for simple and correct grid-based simulations.
2. (Partial) differential equations (PDE) integrations.
3. Linear algebra integrations.
4. Machine learning integrations.
5. Native physics functionality.

[alice-i-cecile]

Moved to #1678; this is approximately impossible to "complete" and so is much better off as a Discussion.