source-sequenceThe two branches select one of four rotation values from the signs of real(z) and imag(z); the carrier update uses that selection with offset / z.
Orbit memory
quadrants
2d237187-b3fd-54e2-8bf4-ef973080f389
Teaching overview
quadrants’ FRM-like/1 source starts z at 0 and carrier at pixel. The loop squares z plus carrier, derives horizontal and vertical from its real and imaginary parts, and uses sign branches to choose a rotation before updating carrier with rotation * offset / z. The bailout is |z| <= 4.
Source walkthrough
frm-v1:a77dc97ca3eff72c3edb9516440760af7d5fdc967d84a7f08bdace726898d79e:loop/4With horizontal > 0, this branch sets rotation to (0, 1) only when vertical > 0 and to (1, 0) only when vertical < 0; zero components leave rotation at (0, 0).
frm-v1:a77dc97ca3eff72c3edb9516440760af7d5fdc967d84a7f08bdace726898d79e:loop/5With horizontal < 0, this branch sets rotation to (-1, 0) only when vertical > 0 and to (0, -1) only when vertical < 0; zero components leave rotation at (0, 0).
frm-v1:a77dc97ca3eff72c3edb9516440760af7d5fdc967d84a7f08bdace726898d79e:loop/6This assignment updates carrier = carrier + rotation * offset / z using the rotation selected by the sign branches.
frm-v1:a77dc97ca3eff72c3edb9516440760af7d5fdc967d84a7f08bdace726898d79e:bailoutThe source keeps iterating only while |z| <= 4.
Syntax features
Parameter experiment
offsetSteps
- Use offset = 0 + 0i at the pinned profile. Keeping center, zoom, rotation, and iterations fixed, change only offset to 1 + 0i and render the trial.
What to observe
For the offset trial, record a visible difference or no visible difference, especially in regions reached through different sign branches.
Exercise
State the four possible rotation values and compare the offset = 0 + 0i and offset = 1 + 0i renders.
Completion check
Your response explains all 4 annotated operations, records the requested comparison, and mentions `rotation * offset / z`.
Sources and rights
Pinned runtime revision a77dc97ca3eff72c3edb9516440760af7d5fdc967d84a7f08bdace726898d79e 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
quadrants
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
- offset: complex
Canonical source
This verified canonical revision is read-only. Remix creates a separate editable fork.
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Source and implementation
- Formula ID
- 2d237187-b3fd-54e2-8bf4-ef973080f389
- Canonical name
- quadrants
- Original name
- quadrants
- Historical source
- Fractint
- Original resource
- fractint-float/formulas/fract003.frmRepository
- 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