Orbit memory

phoenix

e2456b54-ef50-5ac9-9faa-dcb576c5e774

Teaching overview

phoenix is taught from its pinned FRM-like/1 definition. Follow the initial previousZ memory, its phoenixP contribution, and the later memory shift 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-v1:25f923b51ea1e36408f9c48e008187e67a946fc58ef634f93bf0cba216f622aa:init/0
In phoenix, this node executes if ismand: z = 0; otherwise z = pixel.
frm-v1:25f923b51ea1e36408f9c48e008187e67a946fc58ef634f93bf0cba216f622aa:init/1
In phoenix, this node executes previousZ = (0, 0).
frm-v1:25f923b51ea1e36408f9c48e008187e67a946fc58ef634f93bf0cba216f622aa:loop/0
In phoenix, this node executes nextZ = z * z + c + phoenixP * previousZ.
frm-v1:25f923b51ea1e36408f9c48e008187e67a946fc58ef634f93bf0cba216f622aa:bailout
In phoenix, this node executes |z| <= 256.

Syntax features

state-flow

These annotations trace the formula-specific state flow through if ismand: z = 0; otherwise z = pixel; previousZ = (0, 0); nextZ = z * z + c + phoenixP * previousZ.

stopping-test

This annotation is the stopping test, |z| <= 256, rather than a state update.

Parameter experiment

phoenixP

Steps

Run phoenix with the pinned profile and record the result.
Change only phoenixP, keep every other runtime slot and profile control fixed, run again, and record whether a difference occurs.

What to observe

Record whether nextZ = z * z + c + phoenixP * previousZ; previousZ = z; z = nextZ produces a visible-result or |z| <= 256 stopping-behavior difference from the baseline; the pinned definition does not guarantee a difference.

Exercise

Trace phoenix through its annotations, explaining the source operation nextZ = z * z + c + phoenixP * previousZ; previousZ = z; z = nextZ and the stopping test |z| <= 256.

Completion check

Your trace explains all 4 annotations for phoenix, including nextZ = z * z + c + phoenixP * previousZ; previousZ = z; z = nextZ, and distinguishes |z| <= 256 from a state update.

Sources and rights

This teaching unit is grounded in runtime:25f923b51ea1e36408f9c48e008187e67a946fc58ef634f93bf0cba216f622aa and decision:e2456b54-ef50-5ac9-9faa-dcb576c5e774.

rightsStatus is project-owned; implementationBasis is project-owned; publicationDecision is publish; decisionReason is publish-project-owned-native-recipe. This statement does not make broader claims about any third-party original.

Formula Record

phoenix

This canonical FractalPark implementation is published and runnable.

Canonical source

Language: frm-like/1
Standard library: 1
Profile mode: parameter-plane
Profile center: -0.5, 0
Profile zoom: 0.4
Profile iterations: 96
Profile evidence: mechanical

Parameters

phoenixP: real

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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: e2456b54-ef50-5ac9-9faa-dcb576c5e774
Canonical name: phoenix
Original name: phoenix
Historical source: FractalPark
Original resource: public/formula-library/v1/runtime/published/definitions/25f923b51ea1e36408f9c48e008187e67a946fc58ef634f93bf0cba216f622aa.frm Repository
Current implementation: Project-owned

This is a FractalPark project-owned implementation. The linked file is the pinned canonical Definition.

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