FractalPark
Function composition

bali

14d3cb89-d3e7-5bff-b848-af88c9a561ae

Teaching overview

bali’s FRM-like/1 source forms x = 1 / pixel, sets z = x, and sets cclassic = fn1(z). Each loop forms the product (x + cclassic) * (x - cclassic) for z, then replaces x with fn2(z). The bailout is |z| <= 3.

Source walkthrough

  1. frm-v1:459d2a30210e9171b03fb5d7480eeeb22db0051d977a6dc000d39886924a66eb:init/3

    This initialization assignment sets cclassic = fn1(z) after x = 1 / pixel and z = x have been assigned.

  2. frm-v1:459d2a30210e9171b03fb5d7480eeeb22db0051d977a6dc000d39886924a66eb:loop/0

    This loop assignment sets z = (x + cclassic) * (x - cclassic).

  3. frm-v1:459d2a30210e9171b03fb5d7480eeeb22db0051d977a6dc000d39886924a66eb:loop/1

    This following assignment updates x = fn2(z) using the newly computed z.

  4. frm-v1:459d2a30210e9171b03fb5d7480eeeb22db0051d977a6dc000d39886924a66eb:bailout

    The orbit continues only while |z| <= 3.

Syntax features

source-sequence

The product reads the current x and cclassic, and only afterward does fn2 replace x from that product.

Parameter experiment

function1function2

Steps

  1. Use function1 = identity and function2 = identity at the pinned profile. Hold the view fixed, change only function1 to sqr and render; restore it, then change only function2 to sqr and render.

What to observe

For each bali function trial, record a visible difference or no visible difference from the identity baseline.

Exercise

Explain the product and the later x update, then compare one one-slot function trial.

Completion check

Your response explains all 4 annotated operations, records the requested comparison, and mentions `(x + cclassic) * (x - cclassic)`.

Sources and rights

Pinned runtime revision 459d2a30210e9171b03fb5d7480eeeb22db0051d977a6dc000d39886924a66eb 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

bali

This canonical FractalPark implementation is published and runnable.

Deterministic preview of bali

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
  • function2: 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
14d3cb89-d3e7-5bff-b848-af88c9a561ae
Canonical name
bali
Original name
bali
Historical source
Fractint
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