import { type QuadraticIterationOptions } from './complex-quadratic.js';
import type { Point3 } from './sample.js';
export type TricomplexPlatonicSlice3Id = 'airbrot' | 'firebrot' | 'earthbrot';
export interface TricomplexPlatonicSlice3Spec {
    readonly id: TricomplexPlatonicSlice3Id;
    readonly label: string;
    readonly basis: readonly [string, string, string];
    /** Dyadic theorem vertices in the declared basis. */
    readonly vertices: readonly Point3[];
    /** Polygon faces indexing `vertices`. */
    readonly faces: readonly (readonly number[])[];
    readonly center: Point3;
    readonly edgeLength: number;
}
export interface RealMandelbrotParameterEvaluation {
    readonly parameter: number;
    readonly escaped: boolean;
    readonly iterations: number;
    readonly finalValue: number;
    readonly magnitude: number;
}
export interface TricomplexMandelbrotSliceEvaluation3 {
    readonly id: TricomplexPlatonicSlice3Id;
    /** Negative inside, zero on the theorem boundary, positive outside. */
    readonly analyticValue: number;
    readonly analyticallyBounded: boolean;
    readonly escaped: boolean;
    readonly iterations: number;
    /** Four real idempotent factors; Earthbrot's unused fourth factor is zero. */
    readonly factorParameters: readonly [number, number, number, number];
    readonly factors: readonly [
        RealMandelbrotParameterEvaluation,
        RealMandelbrotParameterEvaluation,
        RealMandelbrotParameterEvaluation,
        RealMandelbrotParameterEvaluation
    ];
}
/** Exact theorem data for the three Platonic tricomplex Mandelbrot slices. */
export declare function tricomplexPlatonicSlice3(id: TricomplexPlatonicSlice3Id): TricomplexPlatonicSlice3Spec;
/**
 * The real idempotent parameters whose independent quadratic orbits decide
 * membership in the selected tricomplex Mandelbrot slice.
 */
export declare function tricomplexMandelbrotComponents3(id: TricomplexPlatonicSlice3Id, point: ArrayLike<number>): readonly [number, number, number, number];
/**
 * Exact half-space value for the proven Platonic shape. It is a membership
 * function, not a Euclidean distance outside edges and vertices.
 */
export declare function tricomplexPlatonicValue3(id: TricomplexPlatonicSlice3Id, point: ArrayLike<number>): number;
export declare function containsTricomplexPlatonicSlice3(id: TricomplexPlatonicSlice3Id, point: ArrayLike<number>, epsilon?: number): boolean;
/** Independent real-orbit realization of the tricomplex Mandelbrot theorem. */
export declare function evaluateTricomplexMandelbrotSlice3(id: TricomplexPlatonicSlice3Id, point: ArrayLike<number>, { maxIterations, escapeRadius }?: QuadraticIterationOptions): TricomplexMandelbrotSliceEvaluation3;
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