Rational reciprocal

jm_27

da95ae4b-d401-5eb0-862c-7d977c328fad

Teaching overview

FRM-like/1 defines jm_27 with source initialization z = pixel, then a loop whose first node is sqrz = fn1(z). The pinned parameter-plane profile uses center (0, 0), zoom 0.25, rotation 0, and 96 iterations, and the source tests |z| <= t for bailout.

Source walkthrough

frm-v1:c0fdb8fb46828947defe52dd82bdabd45a1a8baeb32278ae649b7231e647bf2f:init/0
This cited initialization node performs only: z = pixel.
frm-v1:c0fdb8fb46828947defe52dd82bdabd45a1a8baeb32278ae649b7231e647bf2f:loop/0
This cited first loop node performs only: sqrz = fn1(z).
frm-v1:c0fdb8fb46828947defe52dd82bdabd45a1a8baeb32278ae649b7231e647bf2f:bailout
This cited bailout node tests only: |z| <= t.

Syntax features

initialization-flow

The initialization annotation isolates z = pixel rather than a later initialization statement. This is specific to jm_27.

iteration-flow

The iteration annotation isolates the first loop assignment sqrz = fn1(z); jm_27 applies fn1 to z before the reciprocal update. This is specific to jm_27.

bailout-test

The termination annotation identifies the exact continuation comparison |z| <= t. This is specific to jm_27.

Parameter experiment

parameter1function1

Steps

Render jm_27 at the pinned parameter-plane baseline with parameter1 (0, 0), function1 (identity) at their runtime defaults.
Change one of parameter1, function1 at a time, keep center (0, 0), zoom 0.25, rotation 0, and 96 iterations and every other slot fixed, then compare the renderings.

What to observe

For each isolated change to parameter1 or function1, record whether the rendering differs from the baseline and relate the comparison to |z| <= t.

Exercise

For jm_27, use the three annotations to distinguish the single-node operations z = pixel, sqrz = fn1(z), and |z| <= t; explain why no neighboring statement belongs to the loop annotation.

Completion check

Name all 3 annotation IDs, then state exactly that the cited loop node is sqrz = fn1(z) and the cited bailout node is |z| <= t. This completes the jm_27 reading.

Sources and rights

Grounded in runtime source revision c0fdb8fb46828947defe52dd82bdabd45a1a8baeb32278ae649b7231e647bf2f and the publication decision for da95ae4b-d401-5eb0-862c-7d977c328fad.

rightsStatus is source-declared-public-domain-assumption; implementationBasis is direct-adaptation; publicationDecision is publish; decisionReason is publish-census-full-chain-green. These records describe this project decision only and do not assert broader rights in any third-party original.

Formula Record

jm_27

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: family

Parameters

parameter1: complex
function1: function

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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: da95ae4b-d401-5eb0-862c-7d977c328fad
Canonical name: jm_27
Original name: jm_27
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