🏛️ Architect: Traitify TuringSystem for Generic ODE Solver Compatibility

[fderuiter]

This PR refactors math_explorer/src/biology/morphogenesis.rs to align with the "Architect" philosophy of "Traitification".

It makes TuringSystem compatible with the generic ODE solvers (like RungeKutta4) in crate::pure_math::analysis::ode by implementing OdeSystem and TimeStepper.

Crucially, it preserves the highly optimized manual stencil implementation (sliding window, pointer arithmetic) by:

1. Duplicating the stencil logic into derivative_in_place (for generic solvers).
2. Wiring the TimeStepper::step method to call the existing optimized inherent step method (for zero-cost abstraction).

Tests confirm that the system can now be driven by RungeKutta4 (test_turing_structure.rs) while the original optimized step logic remains functional (repro_turing.rs, effectively).

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PR created automatically by Jules for task 11560402969313559583 started by @fderuiter

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[fderuiter]

Run cargo fmt -- --check
Diff in /home/runner/work/math/math/math_explorer/tests/test_turing_structure.rs:1:
#[cfg(test)]
mod tests {

• use math_explorer::biology::morphogenesis::{TuringSystem, TuringState};

• use math_explorer::biology::morphogenesis::{TuringState, TuringSystem};
  use math_explorer::pure_math::analysis::ode::{RungeKutta4, Solver, TimeStepper};

  #[test]
  Diff in /home/runner/work/math/math/math_explorer/tests/test_turing_structure.rs:18:

  // Verify state changed
  let val_after = system.state.u()[50];
  

•    assert!(val_after < 1.0, "Value should have diffused/reacted away from 1.0");
  

•    assert!(
  

•        val_after < 1.0,
  

•        "Value should have diffused/reacted away from 1.0"
  

•    );
  

  }
  }

Error: Process completed with exit code 1.

[google-labs-jules]

Run cargo fmt -- --check
Diff in /home/runner/work/math/math/math_explorer/tests/test_turing_structure.rs:1:
#[cfg(test)]
mod tests {

• use math_explorer::biology::morphogenesis::{TuringSystem, TuringState};

• use math_explorer::biology::morphogenesis::{TuringState, TuringSystem};
  use math_explorer::pure_math::analysis::ode::{RungeKutta4, Solver, TimeStepper};

  #[test]
  Diff in /home/runner/work/math/math/math_explorer/tests/test_turing_structure.rs:18:

  // Verify state changed
  let val_after = system.state.u()[50];
  

•    assert!(val_after < 1.0, "Value should have diffused/reacted away from 1.0");
  

•    assert!(
  

•        val_after < 1.0,
  

•        "Value should have diffused/reacted away from 1.0"
  

•    );
  

  }
  }

Error: Process completed with exit code 1.

Ran cargo fmt to address the formatting issues.