import { ModelSet, type ModelPoint, type WindowBoundaryPolicy } from './model-set.js';
/** The canonical Fibonacci cut-and-project scheme over Z[phi]. */
export declare function createFibonacciModelSet(boundaryPolicy?: WindowBoundaryPolicy): ModelSet;
export type FibonacciTile = 'L' | 'S';
export interface FibonacciPatch {
    /** `tileCount + 1` vertices, beginning at physical coordinate zero. */
    readonly points: readonly ModelPoint[];
    /** One symbol per exact vertex gap: `'L'` for phi^2, `'S'` for phi. */
    readonly tiles: readonly FibonacciTile[];
    /** Points of the underlying sample that landed on the window boundary. */
    readonly boundaryCount: number;
}
/** Prefix of the fixed point of L -> LS, S -> L. */
export declare function fibonacciSubstitutionPrefix(length: number): FibonacciTile[];
/**
 * A symbol-exact finite patch of the canonical Fibonacci model set.
 *
 * @example
 * The tile word is recovered from the geometry rather than rewritten into it.
 * Consecutive vertices, ordered along the one-dimensional physical axis
 * (`parallel[0]`), are separated by exactly two gap lengths whose ratio is
 * the golden ratio; classifying each gap as the longer or shorter one spells a
 * word, and that word is both `tiles` and a prefix of the substitution fixed
 * point — with tile counts that are consecutive Fibonacci numbers:
 * ```ts
 * const patch = fibonacciPatch(13);
 *
 * // Two gap lengths and nothing else, in ratio phi.
 * const gaps = [];
 * let previous = 0;
 * let first = true;
 * for (const point of patch.points) {
 *   const along = Number(point.parallel[0]);
 *   if (!first) gaps.push(along - previous);
 *   previous = along;
 *   first = false;
 * }
 * const long = Math.max(...gaps);
 * const short = Math.min(...gaps);
 * log(gaps.length, (long / short).toFixed(12));       // 13 '1.618033988750'
 *
 * // Classify each gap against the midpoint, and the geometry spells the word.
 * const middle = (long + short) / 2;
 * const recovered = gaps
 *   .map((gap) => (gap > middle ? 'L' : 'S'))
 *   .join('');
 * log(recovered);                                     // 'LSLLSLSLLSLLS'
 * log(recovered === patch.tiles.join(''));            // true
 * log(recovered === fibonacciSubstitutionPrefix(13).join(''));  // true
 *
 * const longs = recovered.split('L').length - 1;
 * log(longs, recovered.length - longs);               // 8 5
 * ```
 */
export declare function fibonacciPatch(tileCount: number): FibonacciPatch;
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