CHAPTER 12 STUDIO
Fractals on graphs, taught through three working labs.
Chapter 11 used pictures and time series. Most enterprise objects worth governing are graphs already: lineage, entity match, hierarchy, dependency. This page walks across the same scale-sensitive descriptors on a different geometry. Sketch a series and see its visibility graph. Pick a network and see its box covers. Click a lineage node and see what breaks downstream.
LAB 1: VISIBILITY GRAPH
Sketch a series. Watch the graph form.
The bars on the left are your series. The graph on the right links any two bars whose tops can see each other without an intermediate bar blocking the line of sight. Toggle a preset, drag a bar, or randomize.
Drag a bar to reshape the series
ready
Edges connect bars with line-of-sight
LAB 2: BOX COVERING
Pick a network. Watch boxes light up at every scale.
For each box size, every node belongs to exactly one box. The number of boxes shrinks as the box size grows. The slope of the log-log fit is the box dimension. The fit is only meaningful when the slope stays stable across multiple box sizes.
Each color is one box at the current size
log-log fit of box count vs box size
LAB 3: LINEAGE RISK
Click a node. See what fails downstream.
Sources sit on the left. Exposures sit on the right. Click any node to inject a defect. The page colors every downstream node it touches and ranks the top-five stewardship priorities by blast-radius spread.
Click a node to inject a defect
CHAPTER MAP
Three bridges. Eight notebooks. One bounded claim.
The chapter does not try to prove enterprise data is fractal. It asks where graph descriptors buy you something ordinary statistics cannot, and it names the failure modes when the descriptors stop being trustworthy.
Why graphs deserve a fractal lens
The framing notebook and the NetworkX primer. The 11.4 union-find work re-expressed as connected components on a thresholded match graph.
Two formal bridges
Visibility graphs (time series to graph). Box covering on graphs (image to graph). Skeleton extraction and renormalization (the test for self-similar structure).
Enterprise translation, then the honesty notebook
Lineage and fault propagation. Entity resolution upgraded with graph descriptors. Four named failure modes that close the cluster.
NOTEBOOK PATH
Open the tracked teaching materials.
The notebooks are the formal teaching spine. This page is the front door.