Function composition

fzpfncoh

0672aed0-1fd1-5acd-9263-a52d5680d3b4

Teaching overview

fzpfncoh’s FRM-like/1 source starts z at pixel and creates a fixed addend f = 1 / cosh(pixel). Each loop applies fn1 to z and then adds f. The bailout bound is |z| <= 50.

Source walkthrough

frm-v1:a2e5619bb8e9528ea042184634f69711d1f7522254d8e39d6060310db4663132:init/1
This initialization assignment fixes f as 1 / cosh(pixel), while z was initialized from pixel.
frm-v1:a2e5619bb8e9528ea042184634f69711d1f7522254d8e39d6060310db4663132:loop/0
This loop assignment replaces z with fn1(z) + f, adding the fixed cosh-based value after the function call.
frm-v1:a2e5619bb8e9528ea042184634f69711d1f7522254d8e39d6060310db4663132:bailout
The bailout permits the orbit while |z| <= 50.

Syntax features

source-sequence

The initialization supplies a fixed cosh-based addend, and the loop combines it with the current fn1(z).

Parameter experiment

function1

Steps

Use function1 = identity at the pinned profile. Keep center, zoom, rotation, and iterations fixed, change only function1 to sqr, and render the trial.

What to observe

Record a visible difference or no visible difference between the identity baseline and the sqr trial, noting the fixed 1 / cosh(pixel) addend.

Exercise

Identify the fixed addend and the function update, then compare identity with sqr.

Completion check

Your response explains all 3 annotated operations, records the requested comparison, and mentions `1 / cosh(pixel)`.

Sources and rights

Pinned runtime revision a2e5619bb8e9528ea042184634f69711d1f7522254d8e39d6060310db4663132 and its publication decision ground this unit.

rightsStatus: source-declared-public-domain-assumption; implementationBasis: direct-adaptation; publicationDecision: publish; decisionReason: publish-census-full-chain-green. This statement makes no broader claim about any third-party original.

Formula Record

fzpfncoh

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

function1: 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: 0672aed0-1fd1-5acd-9263-a52d5680d3b4
Canonical name: fzpfncoh
Original name: fzpfncoh
Historical source: Fractint
Original resource: fractint-float/formulas/fractint.frm Repository
Current implementation: Direct adaptation

The current FractalPark implementation follows the verified semantics of the linked Fractint formula. The original file retains its own rights terms.

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