AI Skill Report Card
Converting Research to Craft Patterns
Quick Start14 / 15
Given a paper or concept (e.g., "hyperbolic paraboloid surfaces"), don't jump straight to stitch counts. First extract the logic primitive — the minimal rule that generates the structure — then map that rule onto a craft's native operations (increases, decreases, row structure).
Input: Paper on hyperbolic tessellations (negative curvature via exponential growth)
Logic primitive: "Add n stitches every row where n grows linearly" → negative curvature
Craft mapping: Crochet — "increase 1 stitch every 2 stitches, repeat each row"
Output: Row-by-row pattern that ruffles like a hyperbolic plane
Recommendation▾
Add a third example showing a failure case or a less clean mapping (e.g., a concept that doesn't translate well) to illustrate judgment calls
Workflow14 / 15
Progress:
- Step 1: Extract the core generative rule from the source material
- Step 2: Strip the rule of domain jargon — state it as abstract logic (sequence, recursion, ratio, transformation)
- Step 3: Identify the craft's native primitives that can express that logic (increase/decrease, cable cross, color change, knot type)
- Step 4: Map each logic unit to a craft operation 1:1
- Step 5: Simulate the pattern mentally (or via gauge swatch) to confirm the geometry emerges
- Step 6: Write the pattern in standard craft notation with the math as an optional sidebar/footnote
- Step 7: Validate scale — adjust for yarn gauge/weight without breaking the ratio from Step 2
Step 1–2 Detail: Extracting the Logic Primitive
Ask: "What is the single rule that, if repeated, produces this structure?" Ignore the paper's proofs, citations, and notation — you want the generative kernel, not the argument. Examples of logic primitives:
- Fibonacci spiral → "each unit's size = sum of previous two"
- Hyperbolic plane → "stitch count grows faster than linear (exponential or compounding increase)"
- Penrose tiling → "two tile shapes with a matching/adjacency constraint, no periodic repeat"
- Möbius strip → "single surface, one half-twist before joining ends"
- Fractal (Koch-like) → "replace each segment with a scaled copy of the generating motif, recurse n times"
Step 3–4 Detail: Craft Primitive Library (reusable across patterns)
| Logic Operation | Crochet | Knitting | Weaving/Macramé |
|---|---|---|---|
| Linear growth | evenly spaced increases | yarn-overs/M1 at intervals | adding warp threads |
| Exponential growth | increase in every stitch, scaling per row | doubling stitch count per row | fanning cord count |
| Recursion/self-similarity | repeat a motif at decreasing scale within itself | nested cable patterns | fractal knot repeats |
| Negative curvature | increases exceed flat-rate (ruffling) | short-row wedges | — |
| Positive curvature | decreases below flat-rate (cupping) | short-row wedges (opposite) | — |
| Topological twist | half-twist join in join round | — | half-twist before Celtic knot closure |
| Periodic tiling | repeat block of n stitches, no boundary condition | charted repeat | regular knot grid |
| Aperiodic tiling | two alternating motifs with adjacency rule | two-motif chart with matching rule | irregular knot grid with rule |
Recommendation▾
Include a brief troubleshooting note on how to handle papers with multiple competing generative rules
Examples18 / 20
Example 1: Input: Research paper on Apollonian gaskets (circles packed recursively in the gaps of larger circles, radius ratio follows Descartes' Circle Theorem). Output:
- Logic primitive: "After placing a circle, pack the largest possible circle into each remaining gap; radius determined by curvature sum formula; recurse."
- Craft mapping (crochet appliqué): Center medallion (crochet circle, radius R). In each gap between it and 3 neighbors, crochet a smaller circle whose chain-start count is scaled by the Descartes ratio (~0.3–0.5x stitch count of parent). Recurse 3 levels deep before gaps become too small to crochet (practical stopping condition replaces infinite recursion).
- Pattern note: "Round 1: mc, 6 sc. Round 2–4: standard circle increases to reach 24 sc (R1). Satellite circles: chain 8, join, sc around (≈8–10 sc, ~0.35R1) — place 3 per gap. Second-generation satellites: chain 4 (~0.15R1) — place in remaining gaps, optional."
Example 2: Input: Paper on the Gömböc (a shape with exactly one stable and one unstable equilibrium — self-righting convex body). Output:
- Logic primitive: "Asymmetric curvature gradient: one axis curves tightly (unstable), the opposite curves shallowly (stable), continuous gradient between."
- Craft mapping (amigurumi): Instead of symmetric decrease rounds at top and bottom, use a steep decrease rate at one pole (6 rounds to close) and a shallow decrease rate at the opposite pole (14 rounds to close), with the equator stitch count matching both tapers at their midpoint.
- Pattern note includes a plotted decrease-rate curve as a visual aid alongside row-by-row instructions.
Recommendation▾
Consider adding a minimal template/checklist for writing the final pattern notation format (row numbering conventions, abbreviations key) to aid completeness
Best Practices
- Decouple the math from the medium early. The logic primitive should be statable in one sentence with zero craft vocabulary and zero paper-specific vocabulary.
- Pick the craft whose native operations best express the primitive, don't force-fit. Exponential growth favors crochet (flat-rate increases compound naturally); linear/periodic structures suit knitting charts or weaving better.
- Preserve ratios, not absolute numbers. Gauge varies by yarn/hook; translate the relationship (e.g., "increase rate 1.5x row rate") so the pattern scales.
- Always include a practical stopping condition for anything recursive/infinite in the source math — craft patterns need a finite row count.
- Keep the math as an annotation, not the instruction. The crafter should be able to follow the pattern with zero math background; the math sidebar is for those who want the "why."
- Swatch-test curvature claims. Mentally simulating stitch growth is a good first pass, but actual gauge/yarn behavior (drape, stiffness) can distort idealized geometry — flag this as a caveat in the pattern.
Common Pitfalls
- Translating notation instead of logic. Don't try to map equations symbol-by-symbol onto stitches — abstract to the generative rule first, or the pattern becomes unknittable.
- Ignoring craft constraints. Stitches are discrete and have minimum/maximum practical increase rates per round (~double per round is roughly the ceiling in crochet before it won't lie flat) — infinite/continuous math must be quantized sensibly.
- Over-literal recursion. True infinite fractals must be truncated — decide the recursion depth based on yarn weight and finished-size constraints, not mathematical purity.
- Forgetting the physical medium fights the math. Yarn has drape and relaxes over time (blocking, gravity) — rigid geometric claims (sharp Penrose vertices, perfect hyperbolic ruffles) will soften; design with that tolerance in mind.
- Writing the pattern before validating the geometry emerges. Always do a quick mental row-count simulation (or small swatch) before finalizing — it's cheaper to catch a logic error at row 3 than after writing the full pattern.