What each Newton step asked of its linear solve, and what the solve cost, under the adaptive policy

At its defaults it draws what each newton step asked of its linear solve, and what the solve cost, under the adaptive policy. The lower series is the tolerance handed to the inner solve at each step and the upper one is the number of conjugate gradient iterations it took. Under the adaptive rule the first step asks for 0.9 and costs 1 iteration, and the last asks for 0.0042 and costs 271. The whole solve costs 1009 inner iterations across 10 Newton steps and ends at a relative residual of 3.37·10⁻¹¹.

forcing-trail is one function in lib/figures/sequence.js — sequences — a solve inside an outer loop, and the accuracy the loop throws away. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

The lower series is the tolerance handed to the inner solve at each step and the upper one is the number of conjugate gradient iterations it took. Under the adaptive rule the first step asks for 0.9 and costs 1 iteration, and the last asks for 0.0042 and costs 271. The whole solve costs 1009 inner iterations across 10 Newton steps and ends at a relative residual of 3.37·10⁻¹¹.

The lower series is the tolerance handed to the inner solve at each step and the upper one is the number of conjugate gradient iterations it took. Under the adaptive rule the first step asks for 0.9 and costs 1 iteration, and the last asks for 0.0042 and costs 271. The whole solve costs 1009 inner iterations across 10 Newton steps and ends at a relative residual of 3.37·10⁻¹¹.

The lower series is the tolerance handed to the inner solve at each step and the upper one is the number of conjugate gradient iterations it took. Under the adaptive rule the first step asks for 10⁻¹⁴ and costs 1775 iterations, and the last asks for 10⁻¹⁴ and costs 1128. The whole solve costs 9358 inner iterations across 9 Newton steps and ends at a relative residual of 1.43·10⁻¹³.

Every figure above checked its own claims on the way to being drawn, and a claim that failed would have stopped the picture rather than shipped a wrong one. Those checks used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

7 distinct claims across 3 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

It draws a decomposition and prints its residual. It calls orderSweep, orderSweep, and every figure above carries the badge — which residualcheck verifies by looking for it in the emitted SVG rather than by finding the call that builds one. A badge that is constructed and then left out of the body is the failure that check exists for.

Across the library: the rule bites on 217 of 397 generators — 199 print a residual and 18 are exempt with a published reason; 180 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.