FractalPark
Rational reciprocal

islandofchaos

0ba0b082-c4b0-51d8-b981-7ca1ca25b9f3

Teaching overview

In FRM-like/1, islandofchaos sets z to seed and roundCount to 1. Each iteration uses earlyTransform(z)+pixel while roundCount is below 10; afterward it uses numeratorTransform(z)/denominatorTransform(z)+pixel, then increments roundCount. The pinned parameter-plane profile uses 96 iterations.

Source walkthrough

  1. frm-v1:46f51a27e66b8e029ee20112496383b57cc510dbfcae0bc63dd9b0a6886dcb8f:init/0

    Initialization: init/0 sets z from seed.

  2. frm-v1:46f51a27e66b8e029ee20112496383b57cc510dbfcae0bc63dd9b0a6886dcb8f:loop/0

    Iteration: loop/0 tests whether roundCount is below 10.

  3. frm-v1:46f51a27e66b8e029ee20112496383b57cc510dbfcae0bc63dd9b0a6886dcb8f:loop/0

    Branch: when roundCount < 10, loop/0 assigns earlyTransform(z)+pixel; otherwise it assigns numeratorTransform(z)/denominatorTransform(z)+pixel.

  4. frm-v1:46f51a27e66b8e029ee20112496383b57cc510dbfcae0bc63dd9b0a6886dcb8f:bailout

    Termination: bailout tests |z| <= real(escapeLimit).

Syntax features

sequence

The cited annotations follow seed initialization, the roundCount < 10 test, and the escapeLimit bailout.

branch

The cited branch selects earlyTransform(z)+pixel before round 10 and numeratorTransform(z)/denominatorTransform(z)+pixel afterward.

Parameter experiment

seedescapeLimitearlyTransformnumeratorTransformdenominatorTransform

Steps

  1. Use the pinned profile as the baseline. Change seed only, keep escapeLimit, earlyTransform, numeratorTransform, and denominatorTransform fixed, run 96 iterations, restore seed, and record whether the result differs.

What to observe

Changing seed may alter the path that reaches the early and later transform branches; record whether a difference occurs.

Exercise

Trace the roundCount < 10 switch and state the assignment on each side.

Completion check

Your trace names all 4 annotations and identifies both branch assignments.

Sources and rights

This teaching unit is grounded in the pinned runtime source revision.

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

Formula Record

islandofchaos

This canonical FractalPark implementation is published and runnable.

Deterministic preview of islandofchaos

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

  • seed: complex
  • escapeLimit: complex
  • earlyTransform: function
  • numeratorTransform: function
  • denominatorTransform: 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
0ba0b082-c4b0-51d8-b981-7ca1ca25b9f3
Canonical name
islandofchaos
Original name
islandofchaos
Historical source
Fractint
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