Algebraic power

rcl_pick10

059080eb-da12-5e85-a1a3-049929bdcf49

Teaching overview

rcl_pick10 is taught from its pinned FRM-like/1 definition. Follow the division by pixel, the subtraction of pixel times sqr(z), and the strict limit 8 as source operations, rather than treating an image as guaranteed. The pinned mechanical profile supplies one concrete viewing setup, not a universal visual prediction.

Source walkthrough

frm-v1:ef31384c340c3899555f3de5048b4c9863b397c767e8ed72cae190d600f3ea48:init/0
In rcl_pick10, this node executes z = pixel.
frm-v1:ef31384c340c3899555f3de5048b4c9863b397c767e8ed72cae190d600f3ea48:loop/0
In rcl_pick10, this node executes z = z / pixel - pixel * sqr(z).
frm-v1:ef31384c340c3899555f3de5048b4c9863b397c767e8ed72cae190d600f3ea48:bailout
In rcl_pick10, this node executes |z| < 8.

Syntax features

state-flow

These annotations trace the formula-specific state flow: z = pixel; z = z / pixel - pixel * sqr(z).

stopping-test

This annotation is the stopping test, |z| < 8, rather than a state update.

Parameter experiment

Steps

Run rcl_pick10 with 64 iterations while keeping the pinned profile’s other controls fixed, and record the result.
Run rcl_pick10 at the pinned profile iteration count of 128, compare the two runs, and record whether a difference occurs.

What to observe

Record whether z = z / pixel - pixel * sqr(z) produces a visible-result or |z| < 8 stopping-behavior difference from the baseline; the pinned definition does not guarantee a difference.

Exercise

Trace rcl_pick10 through its annotations, explaining the source operation z = z / pixel - pixel * sqr(z) and the stopping test |z| < 8.

Completion check

Your trace explains all 3 annotations for rcl_pick10, including z = z / pixel - pixel * sqr(z), and distinguishes |z| < 8 from a state update.

Sources and rights

This teaching unit is grounded in runtime:ef31384c340c3899555f3de5048b4c9863b397c767e8ed72cae190d600f3ea48 and decision:059080eb-da12-5e85-a1a3-049929bdcf49.

rightsStatus is no-explicit-permission; implementationBasis is separated-independent-rewrite; publicationDecision is publish; decisionReason is publish-cleanroom-independent-rewrite-full-chain-green. This statement does not make broader claims about any third-party original.

Formula Record

rcl_pick10

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: 0.5
Profile iterations: 128
Profile evidence: mechanical

Parameters

No declared parameters

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Canonical source

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Source and implementation

Formula ID: 059080eb-da12-5e85-a1a3-049929bdcf49
Canonical name: rcl_pick10
Original name: rcl_pick10
Historical source: Fractint
Original resource: fractint-float/formulas/fract003.frm Repository
Current implementation: Separated independent rewrite

Historical source: Fractint. The current FractalPark implementation is a separated independent rewrite; the original FRM text is not redistributed.

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