Root finding

novaBasin

599a7fda-4c0e-5489-b12e-6e4179ee11f2

Teaching overview

In FRM-like/1, novaBasin initializes z from pixel and replaces |z| below 0.00001 with (0.00001,0). Each loop builds z2 and z3, sets f = z3-(1,0), fp = 3*z2, correction = f/fp, then applies the correction-sized adjustment. The pinned julia profile uses 96 iterations.

Source walkthrough

frm-v1:6864baf1c6fb93ea8ce506200e19583fd0b7c1b361fb17764b661d6424762cfa:init/0
Initialization: init/0 sets z from pixel.
frm-v1:6864baf1c6fb93ea8ce506200e19583fd0b7c1b361fb17764b661d6424762cfa:loop/4
Iteration: loop/4 defines correction = f/fp after the loop has built f and fp.
frm-v1:6864baf1c6fb93ea8ce506200e19583fd0b7c1b361fb17764b661d6424762cfa:init/1
Branch: init/1 tests |z| < 0.00001; its then path replaces z with (0.00001,0).
frm-v1:6864baf1c6fb93ea8ce506200e19583fd0b7c1b361fb17764b661d6424762cfa:bailout
Termination: bailout tests |z - zPrev| >= 0.000001.

Syntax features

sequence

The cited annotations connect z = pixel, correction = f/fp, and the change-based bailout.

branch

The cited branch replaces an initial |z| below 0.00001 with (0.00001,0).

Parameter experiment

Steps

Use the pinned julia profile with all controls fixed. Run 48 iterations and then 96 iterations, and record whether the initial small-|z| replacement or the correction = f/fp update changes the observed iteration counts.

What to observe

The larger cap may expose more correction updates after the initial guard; record whether the iteration counts differ.

Exercise

Explain how correction is defined and what the initialization guard replaces.

Completion check

Your response names all 4 annotations and states correction = f/fp and (0.00001,0).

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

novaBasin

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: 0.35
Profile iterations: 96
Profile evidence: family

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: 599a7fda-4c0e-5489-b12e-6e4179ee11f2
Canonical name: novaBasin
Original name: novaBasin
Historical source: FractalPark
Original resource: public/formula-library/v1/runtime/published/definitions/6864baf1c6fb93ea8ce506200e19583fd0b7c1b361fb17764b661d6424762cfa.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