Transcendental

aa-z-to-z

20e16f12-e0e9-5f56-9364-5c2b60c05f20

Teaching overview

In FRM-like/1, aa-z-to-z initializes z from pixel, then repeatedly assigns exp(z * log(z)). Its bailout compares |z| with real(threshold); the pinned parameter-plane profile uses 96 iterations.

Source walkthrough

frm-v1:cccfbd116d3760e4b3cd57e20f2cb9f5102c7326c75c5d89137be22c2352892c:init/0
Initialization: init/0 sets z from pixel.
frm-v1:cccfbd116d3760e4b3cd57e20f2cb9f5102c7326c75c5d89137be22c2352892c:loop/0
Iteration: loop/0 repeatedly assigns z = exp(z * log(z)).
frm-v1:cccfbd116d3760e4b3cd57e20f2cb9f5102c7326c75c5d89137be22c2352892c:bailout
Termination: bailout tests |z| <= real(threshold).

Syntax features

sequence

The cited annotations connect z = pixel, the repeated exp(z * log(z)) assignment, and the threshold-based bailout.

Parameter experiment

threshold

Steps

Use the pinned profile and its defaults as the baseline. Change threshold only, keep all other controls fixed, run 96 iterations, restore its default, and record whether the result differs.

What to observe

Changing threshold may change which magnitudes pass the bailout test; record whether a difference occurs.

Exercise

Explain which expression updates z and which expression supplies the bailout bound.

Completion check

Your response names all 3 annotations and includes exp(z * log(z)) and real(threshold).

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

aa-z-to-z

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

threshold: complex

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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: 20e16f12-e0e9-5f56-9364-5c2b60c05f20
Canonical name: aa-z-to-z
Original name: aa-z-to-z
Historical source: Fractint
Original resource: fractint-float/formulas/fract001.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