Rational reciprocal

ok-35

0a9a153b-bb4e-53df-9cdf-54fd0ad0081e

Teaching overview

FRM-like/1 defines ok-35 with source initialization z = pixel, then a loop whose first node is mapped = firstMap(z). The pinned parameter-plane profile uses center (0, 0), zoom 0.25, rotation 0, and 96 iterations, and the source tests |z| <= real(threshold) for bailout.

Source walkthrough

frm-v1:0a9786849dd78c3643bae1f6de80fbc42d2e57e50e591090e67d681c81c0822e:init/0
This cited initialization node performs only: z = pixel.
frm-v1:0a9786849dd78c3643bae1f6de80fbc42d2e57e50e591090e67d681c81c0822e:loop/0
This cited first loop node performs only: mapped = firstMap(z).
frm-v1:0a9786849dd78c3643bae1f6de80fbc42d2e57e50e591090e67d681c81c0822e:bailout
This cited bailout node tests only: |z| <= real(threshold).

Syntax features

initialization-flow

The initialization annotation isolates z = pixel rather than a later initialization statement. This is specific to ok-35.

iteration-flow

The iteration annotation isolates the first loop assignment mapped = firstMap(z); ok-35 maps z with firstMap before comparing product and quotient magnitudes. This is specific to ok-35.

bailout-test

The termination annotation identifies the exact continuation comparison |z| <= real(threshold). This is specific to ok-35.

Parameter experiment

multiplierthresholdOffsetfirstMapsecondMap

Steps

Render ok-35 at the pinned parameter-plane baseline with multiplier (0, 0), thresholdOffset (0, 0), firstMap (identity), secondMap (identity) at their runtime defaults.
Change one of multiplier, thresholdOffset, firstMap, secondMap 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 multiplier, thresholdOffset, firstMap, or secondMap, record whether the rendering differs from the baseline and relate the comparison to |z| <= real(threshold).

Exercise

For ok-35, use the three annotations to distinguish the single-node operations z = pixel, mapped = firstMap(z), and |z| <= real(threshold); 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 mapped = firstMap(z) and the cited bailout node is |z| <= real(threshold). This completes the ok-35 reading.

Sources and rights

Grounded in runtime source revision 0a9786849dd78c3643bae1f6de80fbc42d2e57e50e591090e67d681c81c0822e and the publication decision for 0a9a153b-bb4e-53df-9cdf-54fd0ad0081e.

rightsStatus is no-explicit-permission; implementationBasis is separated-independent-rewrite; publicationDecision is publish; decisionReason is publish-cleanroom-independent-rewrite-full-chain-green. These records describe this project decision only and do not assert broader rights in any third-party original.

Formula Record

ok-35

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

multiplier: complex
thresholdOffset: complex
firstMap: function
secondMap: function

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Canonical source

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Source and implementation

Formula ID: 0a9a153b-bb4e-53df-9cdf-54fd0ad0081e
Canonical name: ok-35
Original name: ok-35
Historical source: Fractint
Original resource: fractint-float/formulas/fract196.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