# Spending computation where approximation fails

Can a cheap local approximation identify where expensive computation is actually needed?

Use regularity-sensitive approximation to allocate fine computation to difficult regions of a fractal visualization.

Status: open problem. Formulation and comparisons: reconstruction. Development: historical branch.

## Alternative representations

### Uniform high-resolution computation

Affords: Provides a consistent baseline.

Limits or losses: Spends work in regions where a simpler estimate may suffice.

### Local approximation with refinement

Affords: Allocates work using an estimated error.

Limits or losses: An incorrect error estimator may miss precisely the difficult regions.

## Tension

A cheap indicator must detect its own failure well enough to justify skipping expensive work.

## Challenge

How are missed difficult regions counted alongside runtime savings?

This challenge is an editorial prompt, not a claim that the evidence already resolved it.

## Proposed next move

Benchmark against a high-resolution reference and report both false refinement decisions and final error.

Status: new model-proposed experiment or extension; not a reported result.

## Related problems

- [When to deepen, branch, pause, or return](allocating-exploration.md) — offers an error-guided allocation analogue (retrospective_connection). Local numerical error and research importance both guide where to spend effort, but they are different criteria.

## Evidence anchors

- basis-adaptive-computational-resolution: A proposed experiment uses Taylor approximation in regular regions of a fractal visualization and more detailed computation in regions identified as difficult. The material asks what optimization this might provide and includes reported execution errors while attempting it. [Editorial paraphrase; presence of a proposal does not verify its truth.]

Root evidence and private recovery mappings are not part of this public release.

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