Function composition

birdofprey

09288426-4968-5e78-9ab0-00607cc290bd

Teaching overview

birdofprey’s FRM-like/1 source initializes z from seed. Each iteration squares z, adds pixel inside cosxx, then adds pixel again outside cosxx. The orbit continues while |z| <= 4.

Source walkthrough

frm-v1:dbb90a875ab0a6e56b3210ab8021339e7f9ea19d4bc8f26f82ed22f37ff58ede:init/0
This initialization assignment sets z = seed.
frm-v1:dbb90a875ab0a6e56b3210ab8021339e7f9ea19d4bc8f26f82ed22f37ff58ede:loop/0
This loop assignment replaces z with cosxx(sqr(z) + pixel) + pixel, so pixel is added once inside cosxx and once after it.
frm-v1:dbb90a875ab0a6e56b3210ab8021339e7f9ea19d4bc8f26f82ed22f37ff58ede:bailout
The termination comparison allows another iteration while |z| <= 4.

Syntax features

source-sequence

The loop nests sqr inside cosxx and places a second pixel addition outside that call.

Parameter experiment

seed

Steps

Use seed = 0 + 0i at the pinned profile. Keep center, zoom, rotation, and iterations fixed, change only seed to 1 + 0i, and render the trial.

What to observe

Record a visible difference or no visible difference between the seed baseline and the 1 + 0i trial.

Exercise

Describe the two pixel additions around cosxx, then compare the two seed renders.

Completion check

Your response explains all 3 annotated operations, records the requested comparison, and mentions `cosxx(sqr(z) + pixel)`.

Sources and rights

Pinned runtime revision dbb90a875ab0a6e56b3210ab8021339e7f9ea19d4bc8f26f82ed22f37ff58ede and its publication decision ground this unit.

rightsStatus: no-explicit-permission; implementationBasis: separated-independent-rewrite; publicationDecision: publish; decisionReason: publish-cleanroom-independent-rewrite-full-chain-green. This statement makes no broader claim about any third-party original.

Formula Record

birdofprey

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

seed: complex

Open in Explorer

Canonical source

This verified canonical revision is read-only. Remix creates a separate editable fork.

Loading canonical source…

Source and implementation

Formula ID: 09288426-4968-5e78-9ab0-00607cc290bd
Canonical name: birdofprey
Original name: birdofprey
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