| # Spending computation where approximation fails |
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| Can a cheap local approximation identify where expensive computation is actually needed? |
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| Use regularity-sensitive approximation to allocate fine computation to difficult regions of a fractal visualization. |
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| Status: open problem. Formulation and comparisons: reconstruction. Development: historical branch. |
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| ## Alternative representations |
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| ### Uniform high-resolution computation |
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| Affords: Provides a consistent baseline. |
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| Limits or losses: Spends work in regions where a simpler estimate may suffice. |
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| ### Local approximation with refinement |
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| Affords: Allocates work using an estimated error. |
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| Limits or losses: An incorrect error estimator may miss precisely the difficult regions. |
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| ## Tension |
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| A cheap indicator must detect its own failure well enough to justify skipping expensive work. |
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| ## Challenge |
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| How are missed difficult regions counted alongside runtime savings? |
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| This challenge is an editorial prompt, not a claim that the evidence already resolved it. |
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| ## Proposed next move |
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| Benchmark against a high-resolution reference and report both false refinement decisions and final error. |
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| Status: new model-proposed experiment or extension; not a reported result. |
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| ## Related problems |
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| - [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. |
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| ## Evidence anchors |
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| - 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.] |
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| Root evidence and private recovery mappings are not part of this public release. |
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| [Open in the reader](../index.html#node=adaptive-computational-resolution) · [All problems](../CATALOG.md) |
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