Algebraic power

cubic

17b83663-a502-5e34-bd4c-a116e49eab5f

Teaching overview

cubic is presented from its pinned FRM-like/1 source rather than from its name. The source supplies an initialization block, a loop block, and a bailout test; the pinned profile uses mode parameter-plane; center (-0.5, 0); zoom 0.4; rotation 0; iterations 96. Follow the cited operations to compare repeated runs.

Source walkthrough

frm-v1:581fbcb6400907433c24d3061ac2585a5090574f7ee6e7288bffe177432eaafa:init/0
The init source node begins with `p = pixel`; it establishes the starting path before the loop.
frm-v1:581fbcb6400907433c24d3061ac2585a5090574f7ee6e7288bffe177432eaafa:loop/0
The loop source node executes `z = z * z * z - aa3 * z + b` on each pass.
frm-v1:581fbcb6400907433c24d3061ac2585a5090574f7ee6e7288bffe177432eaafa:bailout
The bailout source node tests `|z| < test`; the iteration continues while that condition holds.

Syntax features

source-sequence

The cited source nodes for cubic—`p = pixel`, `z = z * z * z - aa3 * z + b`, and strict `|z| < test`—form its source-ordered path from setup through update to termination.

Parameter experiment

parameter1

Steps

Begin with the source defaults for parameter1. Change parameter1 from its default (0, 0) to (1, 0). Record the visible result after each single-slot change.

What to observe

Compare the cubic runs and record whether `z = z * z * z - aa3 * z + b` has matching visible results and iteration behavior.

Exercise

Use the cited annotations for cubic—`p = pixel`, `z = z * z * z - aa3 * z + b`, and strict `|z| < test`—to describe the source order.

Completion check

Your response lists the 3 cited annotation IDs and orders cubic’s `p = pixel`, `z = z * z * z - aa3 * z + b`, and strict `|z| < test` from initialization through loop to termination.

Sources and rights

Grounded in the pinned runtime source revision 581fbcb6400907433c24d3061ac2585a5090574f7ee6e7288bffe177432eaafa and its semantic anchors.

rightsStatus: source-declared-public-domain-assumption; implementationBasis: direct-adaptation; publicationDecision: publish; decisionReason: publish-census-full-chain-green. This does not make any broader claim about a third-party original.

Formula Record

cubic

This canonical FractalPark implementation is published and runnable.

Canonical source

Language: frm-like/1
Standard library: 1
Profile mode: parameter-plane
Profile center: -0.5, 0
Profile zoom: 0.4
Profile iterations: 96
Profile evidence: mechanical

Parameters

parameter1: complex

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Canonical source

This verified canonical revision is read-only. Remix creates a separate editable fork.

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Source and implementation

Formula ID: 17b83663-a502-5e34-bd4c-a116e49eab5f
Canonical name: cubic
Original name: cubic
Historical source: Fractint
Original resource: fractint-float/formulas/fractint.frm Repository
Current implementation: Direct adaptation

The current FractalPark implementation follows the verified semantics of the linked Fractint formula. The original file retains its own rights terms.

Rights or attribution concern?

Send the Formula ID and supporting evidence. The maintainer can hold or withdraw the implementation while the claim is reviewed. contact@fractalpark.com