visiter 0.5.1

Build and visualize orbit graphs for discrete iterations under guarded rules.

VisIter

Build and visualize orbit graphs for discrete iterations under guarded rules.

VisIter is a small library that does two complementary things:

1. iterate(start, rules, default=..., max_depth=..., ...) — applies a list of guard-and-operation Rules to seed values via BFS, producing a graph (nodes, edges, per-node depth, optional pseudo-edges marking structural boundaries).

2. to_dot(graph, ...) — turns the graph into a Graphviz Digraph for SVG/HTML/PDF rendering, with anchor/radius cropping, per-rule edge coloring, wedged-pie node fills for branching nodes, and dashed ghost stubs at every kind of cut boundary.

The two are independent: any graph dict that fits the documented shape can be rendered, and iterate can be used purely for graph construction without ever touching the renderer.

Install

pip install visiter

Graphviz must be available on PATH for image rendering (the Python graphviz package wraps the system tool).

Quickstart — descent with divisor rule

A rule that divides by three when applicable, with a +2 fallback for all other values. Every integer path eventually joins one of two small cycles (1 → 3 → 1, 2 → 4 → 6 → 2).

from visiter import iterate, Op, Rule, to_dot

graph = iterate(
    start=range(1, 30),
    rules=[Rule(lambda x: x % 3 == 0, Op(lambda x: x // 3, "÷3"))],
    default=Op(lambda x: x + 2, "+2"),
)
dot = to_dot(graph, anchor=1, radius=8, direction="backward")
dot.render("descent", format="svg")

Quickstart — reverse binary tree with bound

Generate every positive integer up to a ceiling as the binary tree of ×2 / ×2+1 successors of 1. Rule.bound keeps the expansion inside the ceiling; to_dot draws the frontier as dashed ghost stubs.

from visiter import iterate, Op, Rule, to_dot

ceiling = 64

graph = iterate(
    start=[1],
    rules=[
        Rule(lambda x: True,
             Op(lambda x: 2 * x, "×2"),
             bound=lambda x: 2 * x <= ceiling),
        Rule(lambda x: True,
             Op(lambda x: 2 * x + 1, "×2+1"),
             bound=lambda x: 2 * x + 1 <= ceiling),
    ],
    default=None,
)
dot = to_dot(graph, show_binary=True)
dot.render("binary_tree", format="svg")

CLI

A single visiter command with subcommands. Each subcommand takes its function's keyword arguments as a single Python expression that is eval'd in a namespace where Op, Rule, iterate, and to_dot are pre-bound. Output is JSON (iterate) and DOT (to-dot) on stdout, so they pipe directly:

visiter iterate 'range(1, 30),
                 [Rule(lambda x: x%3==0, Op(lambda x: x//3, "÷3"))],
                 default=Op(lambda x: x+2, "+2")' \
  | visiter to-dot 'anchor=1, radius=8, direction="backward"' \
  | dot -Tsvg > descent.svg

The validate subcommand checks a graph JSON document against the bundled JSON Schema (schemas/v1/graph.schema.json, Draft 2020-12):

pip install visiter[validate]
visiter iterate '...' | visiter validate

The analyze subcommand bridges to NetworkX so you can run any of its hundreds of graph algorithms on the output (cycles, shortest paths, centrality, strongly-connected components, ...) — and when the algorithm returns a NetworkX graph itself, it flows straight back into visiter to-dot:

pip install visiter[analytics]
visiter iterate '...' \
  | visiter analyze 'nx.condensation(graph)' \
  | visiter to-dot '' | dot -Tsvg > scc.svg

Why VisIter?

The short pitch: VisIter is free, scriptable, Graphviz-native, Unix-pipe-composable orbit-graph rendering for discrete iterations under guarded rules — with cutoff boundaries (bounds, depth limits, render crops) as a first-class visual primitive, not silent truncation.

If you have a Mathematica license, NestGraph covers the core BFS. For term rewriting with equational theories, use Maude. For Petri-net reachability, LoLA. For generic graph analytics, NetworkX. For the specific combination of "Python + rule-driven reachability from a seed + opinionated rendering + shell pipes", the niche is small but real.

Full honest comparison against NetworkX, NestGraph, Maude, LoLA, and continuous-dynamics tooling: docs/comparison.md.

Documentation

• docs/tutorial.md — gentle introduction: what problem the tool solves, smallest example, what each piece does, what the dashed arrows mean. Start here.
• docs/manual.md — reference: every parameter, every data field, the rendering model in full, design decisions.
• docs/comparison.md — how VisIter relates to other tools in the ecosystem, and when to pick something else.
• demos/ — runnable end-to-end examples: make demo writes SVG/PDF/DOT into demos/out/.

License

MIT