Transcendental

fzppcoct

028a6158-e5dd-5d63-a5a7-5db2e3f7d87d

Teaching overview

FRM-like/1 defines fzppcoct with source initialization z = pixel, then a loop whose first node is z = cosxx(z) + offset. The pinned parameter-plane profile uses center (-0.5, 0), zoom 0.4, rotation 0, and 96 iterations, and the source tests |z| <= 50 for bailout.

Source walkthrough

frm-v1:77c461de2d9cf0bbfb4a3257fb4e83bd1f250f6f5f1c52020ff3da0ecee366d9:init/0
This cited initialization node performs only: z = pixel.
frm-v1:77c461de2d9cf0bbfb4a3257fb4e83bd1f250f6f5f1c52020ff3da0ecee366d9:loop/0
This cited first loop node performs only: z = cosxx(z) + offset.
frm-v1:77c461de2d9cf0bbfb4a3257fb4e83bd1f250f6f5f1c52020ff3da0ecee366d9:bailout
This cited bailout node tests only: |z| <= 50.

Syntax features

initialization-flow

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

iteration-flow

The iteration annotation isolates the first loop assignment z = cosxx(z) + offset; fzppcoct replaces z with cosxx(z) plus the precomputed offset. This is specific to fzppcoct.

bailout-test

The termination annotation identifies the exact continuation comparison |z| <= 50. This is specific to fzppcoct.

Parameter experiment

Steps

Render fzppcoct with the pinned parameter-plane baseline: center (-0.5, 0), zoom 0.4, rotation 0, and 96 iterations.
Keep center (-0.5, 0), zoom 0.4, rotation 0, and 96 iterations fixed except for iterations, render once at 48 iterations, and compare it with the 96-iteration baseline.

What to observe

Record whether the 48- versus 96-iteration comparison changes anything, and note the source limit |z| <= 50. This is the fzppcoct comparison.

Exercise

For fzppcoct, use the three annotations to distinguish the single-node operations z = pixel, z = cosxx(z) + offset, and |z| <= 50; 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 z = cosxx(z) + offset and the cited bailout node is |z| <= 50. This completes the fzppcoct reading.

Sources and rights

Grounded in runtime source revision 77c461de2d9cf0bbfb4a3257fb4e83bd1f250f6f5f1c52020ff3da0ecee366d9 and the publication decision for 028a6158-e5dd-5d63-a5a7-5db2e3f7d87d.

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

fzppcoct

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

No declared parameters

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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: 028a6158-e5dd-5d63-a5a7-5db2e3f7d87d
Canonical name: fzppcoct
Original name: fzppcoct
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