Algebraic power

chebyshev2

09ee96d1-18a8-5dad-83e1-d05f0c59be4b

Teaching overview

chebyshev2 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:ab0bdc1929dee1daeb9486d7b1fd885a6644367232854694fa88908eb4e6c0ce:init/0
The init source node begins with `if ismand`; it establishes the starting path before the loop.
frm-v1:ab0bdc1929dee1daeb9486d7b1fd885a6644367232854694fa88908eb4e6c0ce:loop/0
The loop source node executes `z = 2 * (z * z) - (1, 0) + c` on each pass.
frm-v1:ab0bdc1929dee1daeb9486d7b1fd885a6644367232854694fa88908eb4e6c0ce:bailout
The bailout source node tests `|z| <= 256`; the iteration continues while that condition holds.

Syntax features

source-sequence

The cited source nodes for chebyshev2—`if ismand`, `z = 2 * (z * z) - (1, 0) + c`, and `|z| <= 256`—form its source-ordered path from setup through update to termination.

Parameter experiment

Steps

Use the pinned profile (mode parameter-plane; center (-0.5, 0); zoom 0.4; rotation 0; iterations 96). Run it once and record the visible result, then repeat with the same profile.

What to observe

Compare the chebyshev2 runs and record whether `z = 2 * (z * z) - (1, 0) + c` has matching visible results and iteration behavior.

Exercise

Use the cited annotations for chebyshev2—`if ismand`, `z = 2 * (z * z) - (1, 0) + c`, and `|z| <= 256`—to describe the source order.

Completion check

Your response lists the 3 cited annotation IDs and orders chebyshev2’s `if ismand`, `z = 2 * (z * z) - (1, 0) + c`, and `|z| <= 256` from initialization through loop to termination.

Sources and rights

Grounded in the pinned runtime source revision ab0bdc1929dee1daeb9486d7b1fd885a6644367232854694fa88908eb4e6c0ce and its semantic anchors.

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

Formula Record

chebyshev2

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: 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: 09ee96d1-18a8-5dad-83e1-d05f0c59be4b
Canonical name: chebyshev2
Original name: chebyshev2
Historical source: FractalPark
Original resource: public/formula-library/v1/runtime/published/definitions/ab0bdc1929dee1daeb9486d7b1fd885a6644367232854694fa88908eb4e6c0ce.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