Detail Has a Scale, Not a Moral Value
08 November 2026
Visual-computation research note

Abstract
A surface can become harder to understand as more detail is added. CalcuArt v2.3 treats marks and patterns as structured objects with scale, orientation, topology and provenance, rather than as a single richness setting. This note examines the practical consequence: a multiscale design should preserve meaningful relationships while changing the amount of detail visible at a particular viewing size. It proposes an evaluation, not a report of an implemented renderer. [1, original p. 4, §3.2]

Start with one line
An unoriented line at angle θ is equivalent to one at θ+π. Recording the angle as an ordinary scalar can make nearly identical orientations appear far apart at the boundary of the chosen interval. The source instead represents orientation with (cos 2θ, sin 2θ). The doubled angle gives the same pair after a half-turn, eliminating that artificial discontinuity. This does not remove genuine changes in a pattern; it removes a mismatch between the representation and the geometry. [1, p. 4]

The distinction matters when averaging directions across a surface. A naive arithmetic average of angles just below π and just above zero points toward the wrong orientation. Averaging their doubled-angle vectors is more appropriate, although a near-zero resultant still leaves the direction ambiguous. That ambiguity is information. It should not be replaced by a confident arbitrary arrow.

From repetition to hierarchy
PatternIR includes motif identity, support charts, adjacency, repetition groups, periods, phase fields and a scale hierarchy. CalcuArt supplies an illustrative local texture channel, a sum of cosines whose wave vectors carry cycles per meter. Its amplitudes carry the output-channel units and its phases are in radians. This dimensional discipline prevents a physical repetition period from being silently confused with a pixel spacing. [1, p. 4]

The cosine model is deliberately limited. A weave, a knot and a culturally specific emblem may share similar spatial frequencies while differing in connectivity, construction and meaning. Discrete topology and symbolic records therefore remain necessary. A frequency spectrum alone cannot certify that the right motif was preserved, and a symmetry group cannot establish cultural provenance or permission to reuse a symbol.

When the window shrinks
Imagine a broad motif containing a smaller repeated border. On a large display, both structures may be legible. On a small display, the border can turn into a vibrating band or disappear. A renderer must then decide what to preserve: literal strokes, the perceived border width, or a simplified version of the repeating relation. These are different design goals, not interchangeable descriptions of accuracy.

A proposed implementation would record the physical or image-space scale of each mark, the viewing transform and the smallest intended feature. It would then create several display-size variants while preserving declared structural invariants. Filtering and sampling choices would be documented rather than credited to a general promise of continuity. No such variants were rendered or measured for this article.

Attention is a separate hypothesis
The adjacent attention model distinguishes desired, predicted and measured attention. A normalized density or a softmax over saliency logits can express where a system predicts emphasis, but it does not demonstrate where viewers look. The source identifies gaze traces, task performance and blinded comparisons as possible empirical evidence. [1, original pp. 4–5, §3.3]

This suggests a controlled question: does simplifying a fine border improve recognition of the main motif without changing the intended hierarchy? Compare matched layouts at fixed viewing sizes. Record identification errors, response time and participant judgments separately. A saliency score may help formulate the hypothesis, but it should not stand in for those outcomes. Population and task must be declared because inspection by a specialist differs from casual viewing.

What would count as success?
A useful system would retain the declared relationships across scale while stating what detail was removed. It would not receive automatic credit for more marks, stronger contrast or higher spectral energy. The source calls “intricacy without clutter” a contextual aim, not an identity between two numbers. Scale ranges organize decisions; they are not instructions to maximize texture everywhere. [1, p. 4]

Conclusion
Multiscale design is an exercise in selective preservation. Orientation, spacing and topology can be represented explicitly; meaning and attention require additional evidence. The strongest result would be a legible transformation with visible assumptions, not a claim that detail itself is quality.

Reference
[1] CalcuArt v2.3, Calculus Only, 7 November 2026, §§3.2–3.3, original PDF pp. 4–5. The supplied excerpt contains those pages. Display-size experiments and implementation choices above are proposals.
