FractalPark
Function composition

flyc

06504747-8ee8-5c39-869b-8b3a992e8c24

Teaching overview

flyc’s FRM-like/1 source initializes z from seed. Each loop records coordinate = real(z), then replaces z with firstTransform(z) + pixel and again with secondTransform(z) - pixel. The bailout uses the dynamic threshold real(limit): |z| <= real(limit).

Source walkthrough

  1. frm-v1:9550f75ecdb596526b8a5c980361843f70210a5bb6c19a90746736acb8f8faac:loop/0

    This assignment stores coordinate = real(z); no later source assignment reads coordinate.

  2. frm-v1:9550f75ecdb596526b8a5c980361843f70210a5bb6c19a90746736acb8f8faac:loop/1

    This loop assignment sets z = firstTransform(z) + pixel.

  3. frm-v1:9550f75ecdb596526b8a5c980361843f70210a5bb6c19a90746736acb8f8faac:loop/2

    This next assignment uses that updated z and sets z = secondTransform(z) - pixel.

  4. frm-v1:9550f75ecdb596526b8a5c980361843f70210a5bb6c19a90746736acb8f8faac:bailout

    The termination comparison uses real(limit) as the bound: |z| <= real(limit).

Syntax features

source-sequence

The coordinate assignment only records real(z); the two transforms run in sequence, and the termination bound is real(limit).

Parameter experiment

seedlimitfirstTransformsecondTransform

Steps

  1. Use seed = 0 + 0i, limit = 0 + 0i, firstTransform = identity, and secondTransform = identity at the pinned profile. Keep all controls fixed, change only seed to 1 + 0i and render; restore it, then change only limit to 4 + 0i and render; restore it, then change only firstTransform to sqr and render; restore it, then change only secondTransform to sqr and render.

What to observe

For each flyc one-slot trial, record a visible difference or no visible difference; the limit trial changes the bound through real(limit).

Exercise

Explain the sequential transforms and real(limit) bailout, then compare the baseline with one one-slot trial.

Completion check

Your response explains all 4 annotated operations, records the requested comparison, and mentions `real(limit)`.

Sources and rights

Pinned runtime revision 9550f75ecdb596526b8a5c980361843f70210a5bb6c19a90746736acb8f8faac 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

flyc

This canonical FractalPark implementation is published and runnable.

Deterministic preview of flyc

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

  • seed: complex
  • limit: complex
  • firstTransform: function
  • secondTransform: function
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Canonical source

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Source and implementation

Formula ID
06504747-8ee8-5c39-869b-8b3a992e8c24
Canonical name
flyc
Original name
flyc
Historical source
Fractint
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