Root finding

newton4

75e70076-b422-5535-b3c9-c484fbf879e6

Teaching overview

In FRM-like/1, newton4 initializes z from pixel. The loop builds z2, z3, and z4, then assigns numerator/denominator = (3*z4+(1,0))/(4*z3). The pinned parameter-plane profile uses 96 iterations.

Source walkthrough

frm-v1:be9ade0f6d4b272ca864da504bb66a6abab234322112686e72e1624353ce11ec:init/0
Initialization: init/0 sets z from pixel.
frm-v1:be9ade0f6d4b272ca864da504bb66a6abab234322112686e72e1624353ce11ec:loop/0
Iteration: loop/0 sets z2 = z*z; later loop nodes build z3, z4, numerator, and denominator before assigning their quotient.
frm-v1:be9ade0f6d4b272ca864da504bb66a6abab234322112686e72e1624353ce11ec:bailout
Termination: bailout tests |z - zPrev| >= 0.000001.

Syntax features

sequence

The cited annotations connect z = pixel, the z2/z3/z4 construction leading to numerator/denominator, and the change-based bailout.

Parameter experiment

Steps

Use the pinned profile with all controls fixed. Run 48 iterations and then 96 iterations, and record whether the z2/z3/z4 quotient update changes the observed iteration counts.

What to observe

The larger cap may expose further applications of the degree-four quotient update; record whether the iteration counts differ.

Exercise

List the intermediate powers that precede the numerator/denominator assignment.

Completion check

Your response names all 3 annotations and lists z2, z3, and z4.

Sources and rights

This teaching unit is grounded in the pinned runtime source revision.

rightsStatus is project-owned; implementationBasis is project-owned; publicationDecision is publish; decisionReason is publish-project-owned-native-recipe. This does not make a broader claim about any third-party original.

Formula Record

newton4

This canonical FractalPark implementation is published and runnable.

Canonical source

Language: frm-like/1
Standard library: 1
Profile mode: parameter-plane
Profile center: 0, 0
Profile zoom: 0.25
Profile iterations: 96
Profile evidence: mechanical

Parameters

No declared parameters

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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: 75e70076-b422-5535-b3c9-c484fbf879e6
Canonical name: newton4
Original name: newton4
Historical source: FractalPark
Original resource: public/formula-library/v1/runtime/published/definitions/be9ade0f6d4b272ca864da504bb66a6abab234322112686e72e1624353ce11ec.frm Repository
Current implementation: Project-owned

This is a FractalPark project-owned implementation. The linked file is the pinned canonical Definition.

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