R60 · visual algorithm laboratory

Seven algorithms, held against the same world.

This page fixes the concept snapshot, selected origins, world coordinates, similarity matrix, and three-hop limit. It changes the connectivity algorithm, then repeats the comparison through three presentation grammars. The goal is not to crown the prettiest image. It is to see which visual consequences are evidence, which are topology, and which are artifacts of the drawing.

Open the live ego map Read the visual report Open notebook

Algorithms: 7
Diagnostic origins: 4
Presentation grammars: 3
Visible cutoff: 0.10

World field

All panels reuse Mutual-neighbor force coordinates. More colored area means greater visual footprint, not greater metric distance.

Affinity profile

Every concept is placed on one shared high-to-low origin-similarity axis, removing the two-dimensional layout as an explanation.

Depth band

Nodes move only by hop depth while their vertical order remains tied to the fixed world, exposing branch fan-out and propagation.

1. Aligned world fields

Read each row horizontally. Faint gray dots are the complete 185-concept context; colored dots are reached nodes; dot size and opacity encode strength; lines show direct relations only. A blank panel is a measured isolate, not a missing rendering.

Weak forced edge · C040

Its sixth-ranked relation is only 0.383; the rank lens still draws six direct relations.

Nearest six · path product

baseline

degree 6 · reach 62 · visible 58

Cosine ≥ 0.60 · path product

keep

degree 0 · reach 1 · visible 0

Mutual nearest

candidate

degree 0 · reach 1 · visible 0

Nearest-six reach · origin affinity

keep

degree 6 · reach 62 · visible 2

Nearest-six reach · path cohesion

experimental

degree 6 · reach 62 · visible 49

Weakest-link path

candidate

degree 6 · reach 62 · visible 30

Multipath support

candidate

degree 6 · reach 62 · visible 58

Threshold boundary isolate · C150

Its strongest relation is 0.597, below the fixed threshold, so the absolute lens draws none.

Nearest six · path product

baseline

degree 6 · reach 47 · visible 46

Cosine ≥ 0.60 · path product

keep

degree 0 · reach 1 · visible 0

Mutual nearest

candidate

degree 1 · reach 13 · visible 12

Nearest-six reach · origin affinity

keep

degree 6 · reach 47 · visible 24

Nearest-six reach · path cohesion

experimental

degree 6 · reach 47 · visible 46

Weakest-link path

candidate

degree 6 · reach 47 · visible 46

Multipath support

candidate

degree 6 · reach 47 · visible 46

Dense threshold region · C012

It has 46 direct relations at the fixed threshold, showing why absolute topology can saturate.

Nearest six · path product

baseline

degree 6 · reach 19 · visible 18

Cosine ≥ 0.60 · path product

keep

degree 46 · reach 114 · visible 113

Mutual nearest

candidate

degree 6 · reach 18 · visible 17

Nearest-six reach · origin affinity

keep

degree 6 · reach 19 · visible 18

Nearest-six reach · path cohesion

experimental

degree 6 · reach 19 · visible 18

Weakest-link path

candidate

degree 6 · reach 19 · visible 18

Multipath support

candidate

degree 6 · reach 19 · visible 18

Largest reach divergence · C143

Three-hop reach changes from 18 to 114 when membership changes from rank to absolute similarity.

Nearest six · path product

baseline

degree 6 · reach 18 · visible 17

Cosine ≥ 0.60 · path product

keep

degree 38 · reach 114 · visible 113

Mutual nearest

candidate

degree 6 · reach 18 · visible 17

Nearest-six reach · origin affinity

keep

degree 6 · reach 18 · visible 17

Nearest-six reach · path cohesion

experimental

degree 6 · reach 18 · visible 17

Weakest-link path

candidate

degree 6 · reach 18 · visible 17

Multipath support

candidate

degree 6 · reach 18 · visible 17

2. Remove the map and inspect the field

The same results are now strips ordered once by direct cosine similarity to the selected origin. Hard cutoffs appear as missing cells, while scoring algorithms appear as different gradients over comparable membership.

Weak forced edge · C040

Centralized/local food systems

Threshold boundary isolate · C150

Post-Car Choreographed Flow City

Dense threshold region · C012

AI-Externalized Thought Flow

Largest reach divergence · C143

Persistent AI-Mediated Externalized Cognition Loop

3. Make propagation visible

Two extrema are redrawn as hop bands. The weak-edge case tests whether an algorithm can admit emptiness; the dense-threshold case tests whether it remains readable when an absolute component fans out.

Weak forced edge · C040

Centralized/local food systems

Nearest six · path product

baseline

depths 6 / 18 / 37

Cosine ≥ 0.60 · path product

keep

depths 0 / 0 / 0

Mutual nearest

candidate

depths 0 / 0 / 0

Nearest-six reach · origin affinity

keep

depths 6 / 18 / 37

Nearest-six reach · path cohesion

experimental

depths 6 / 18 / 37

Weakest-link path

candidate

depths 6 / 18 / 37

Multipath support

candidate

depths 6 / 18 / 37

Dense threshold region · C012

AI-Externalized Thought Flow

Nearest six · path product

baseline

depths 6 / 4 / 8

Cosine ≥ 0.60 · path product

keep

depths 46 / 51 / 16

Mutual nearest

candidate

depths 6 / 4 / 7

Nearest-six reach · origin affinity

keep

depths 6 / 4 / 8

Nearest-six reach · path cohesion

experimental

depths 6 / 4 / 8

Weakest-link path

candidate

depths 6 / 4 / 8

Multipath support

candidate

depths 6 / 4 / 8

What the algorithms do visually

Thresholding creates a visual phase change

The same absolute arm draws 0 visible non-root nodes for C040 and 113 for C012.

Origin affinity can make graph reach nearly disappear

For C040, ranked membership reaches 62 nodes, but only 2 non-root nodes remain above the declared 0.10 display cutoff.

Multipath support turns convergence into brightness

In the dense case, field mass rises from 10.2 under one selected path to 14.2 when all simple routes contribute.

Algorithm ledger

The numerical columns summarize only the four declared diagnostic origins. They measure the rendered fields; they are not population estimates for all concepts.

Algorithm	Visual result	Median reach	Median visible	Median field mass	Caution
Nearest six · path product bounded navigational identity; membership does not claim that the sixth neighbor is absolutely close	A medium-sized, evenly branched footprint whose fading is mostly a record of hop count.	33.0	32.0	11.2	The regular footprint is partly guaranteed by fixed out-degree.
Cosine ≥ 0.60 · path product absolute connectivity; concepts with no qualifying edge remain visibly isolated and dense regions may have more than six edges	Either a blank field or a saturated component: the visual bifurcation is the evidence this lens contributes.	57.5	56.5	27.4	One cutoff can turn a continuous boundary into a hard cliff.
Mutual nearest Keep a ranked edge only when both endpoints choose each other.	Small reciprocal islands with fewer one-way spokes and visibly harder boundaries.	15.5	14.5	6.9	Reciprocity can reject a real relation near a dense hub.
Nearest-six reach · origin affinity bounded reach membership with intensity set by each reached concept's direct cosine similarity to the selected origin	A bounded footprint with distant-in-meaning members fading out even when the traversal can still reach them.	33.0	17.5	9.2	Fading says direct root affinity, not path unreliability.
Nearest-six reach · path cohesion bounded reach membership with intensity set by the candidate's mean cosine similarity to every earlier concept on its chosen path	Broad, comparatively even halos because a candidate can agree with the route context despite weak direct origin affinity.	33.0	32.0	13.0	A mean can conceal a single weak bridge.
Weakest-link path Let the weakest edge cap every selected route.	Branch-level plateaus: one weak bridge dims every descendant beyond it.	33.0	24.0	13.9	One noisy edge can suppress an otherwise coherent route.
Multipath support Accumulate support from every simple route within three hops.	Bright convergence hotspots where several routes support the same target; redundant hubs can quickly saturate.	33.0	32.0	19.2	The probability-union display treats correlated paths as support.