The figure library
No figure on this site is a drawing that was made once and saved. Each one is a function: it takes a divergence angle, a rise, a point count or an exponent and returns SVG, so the same generator draws the head at 137.5° and the head at 99.5° without either being redrawn, and the difference between the two plates is a difference between two numbers rather than between two drawings.
That is also why nothing here is drawn by hand, in the strong sense. Every point a figure places arrives from the lattice, the placement rule or one of the other libraries behind this collection, computed from a stated rule — and the counting machinery is never shown the angle that produced the points, which is what makes a count of 34 evidence rather than a restatement. There are 101 generators so far, reached for by 365 essays in 602 distinct pairings — counting an essay once per generator it calls, however many figures it draws with it.
Reuse is the number that decides whether any of this is sustainable, which is why it is published rather than kept in a plan. A generator written for one essay and never called again is a design failure and not a neutral cost. The count beside each name is how many essays instantiate it, and a standing check refuses to let the work ledger advance if the ratio falls.
It is also the blast radius. Changing a generator changes every figure in its list at once, so that list is what has to be rebuilt and looked at before the change is believed — a bad shared helper once broke a hundred and eighty-one figures across four of these sites, and was caught only because somebody rebuilt immediately and knew where to look.
Each generator has its own page, drawn at its defaults — which is almost never how an essay calls it, since a placement states the numbers that essay is arguing about. Every one of the 602 pairings passes some, and that fraction is a measurement this site keeps: it drew 0% of its figures at the numbers its own essays argue about until a repair pass in August 2026, and has held at essentially 100% since.
Each page also lists the options its generator actually reads, and that list is
the one thing here worth checking a placement against. An option a placement passes that the
function does not read is silently ignored: the figure draws its defaults under a caption
describing something else, and every other gate passes on it — the SVG is well formed, its
labels fit and contrast, and it renders in a real browser. That is not hypothetical. On the day
this check was adopted here it found five such placements, one of them asking a transport model
for sixty cells by passing n to a function spelling it N.
Heads, and counting them
1 generator
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counted-spirals20 essays
The two spiral families a counter finds between 0.43 and 0.67 of the radius
Stems, and the ladder
1 generator
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hop-lengths42 essays
Which offsets give short hops, at a rise of 0.05
Cones and other surfaces
1 generator
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rise-up-the-cone6 essays
The rise falls as one over the distance from the apex
Whorls, and patterns with k at a time
1 generator
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jugate-stems16 essays
three stems: 1, 2, 3 primordia at a time
Where the angle comes from
1 generator
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the-rule11 essays
The rule, 26 steps in, at a growth of 0.40
The same pattern with a rate
1 generator
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growing-stem10 essays
A stem grown at 92 nodes per rung
Noise, and where it gets in
1 generator
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noise-fate-map6 essays
What becomes of a seeded branch at 65 nodes per rung
Noise that arrives through the neighbours
1 generator
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basin-changes9 essays
Placements that went to a different minimum, per thousand
The order of the divergences
1 generator
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the-sequence-remembers9 essays
The memory of a divergence sequence, at 0.75° of scatter
The count, read out of the angles
1 generator
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the-spectrum-names-the-family4 essays
The order of the angles carries the count
The neighbourhood, swept
1 generator
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the-neighbourhood-that-changes-nothing2 essays
A sixfold neighbourhood, and nothing to dilute
What a mean side count throws away
1 generator
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six-and-the-second-moment4 essays
The statistic everybody reports is the one that cannot vary
Why two counts are enough
1 generator
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families-are-sums5 essays
Every family but two is the sum of two others
The pair, out of the angles
1 generator
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two-combs17 essays
Two combs, at a rise of 0.005
The disorder, swept over the angle
1 generator
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disorder-against-angle7 essays
The disorder of a head against its divergence angle, 300 points
Two statistics of one sequence
1 generator
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both-statistics4 essays
Both statistics, on the same stems, at a rise of 0.005
Which junctions say anything
2 generators
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the-band-decides-the-answer1 essay
A tree built at an exponent of 3, measured band by band -
which-junctions-say-anything4 essays
The uninformative sample does not say so — it says something else
How far the rule reaches
1 generator
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neighbours-with-distance9 essays
A stem gathers neighbours linearly; a growing disc barely gathers them at all
A neighbourhood written down as a claim
1 generator
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cut-shapes5 essays
Three cut-offs at the same nominal width of 3 spacings
Organs with no single exponent
1 generator
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rings-not-geometric4 essays
An ogive's rings are not a fixed factor apart
What a plant might be doing
1 generator
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dispersion-curve6 essays
Which patterns grow on a ring of circumference 1.40
Shells and growth
1 generator
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raup-shell8 essays
A shell section at W = 2.40, D = 0.42
Branching and transport
4 generators
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fitted-exponent3 essays
The exponent fitted from the junctions, rather than assumed -
l-system5 essays
An L-system after 4 rewrites of two rules -
murray-tree10 essays
A branching tree in which every junction obeys the cube law -
why-three3 essays
The two costs, and where their sum is least
Packing and tiling
1 generator
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cells-of-a-head11 essays
Voronoi cells of a head at 137.51°
The claims, measured
1 generator
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where-the-claim-holds5 essays
The version of the claim that does survive measurement
The survey this site has not done
1 generator
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what-a-count-is-worth8 essays
A count of m and n pins the divergence to 221°/mn
What a disturbance's own structure can forge
2 generators
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comb-ratio5 essays
The two combs, in the proportions the rule gives them -
forged-spectrum11 essays
A lattice with an error inherited from the two contact neighbours
Two windows on one climbing stem
1 generator
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two-windows5 essays
Two windows on a shoot at 400 nodes per rung
The dip at a large denominator
1 generator
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background-neighbourhood7 essays
The neighbourhood of 21/55, and where its background was taken from
The rung, the window and the sample grid
1 generator
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what-the-grid-decides3 essays
What the finer grid does to the rises already published
Take an organ away, and watch
1 generator
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cut-by-offset13 essays
The next organ moves for the last 13, and for no others
The ratio, across a rung
1 generator
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ratio-across-a-rung4 essays
The ratio is a U across every rung, and its floor is the number that was reported
One denominator, four fractions
1 generator
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same-denominator2 essays
Four fractions of 55, one width
What the rule does with a coloured disturbance
1 generator
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survives-by-colour5 essays
What a lattice survives depends on the colour of the disturbance, sixfold
The front, rung by rung
1 generator
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two-slots13 essays
Two answers 138° apart, and one organ holding the second one up
The dip, integrated
1 generator
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width-by-window6 essays
The area never settles, so the number reported is the window
A disturbance with no history
1 generator
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what-sharing-costs3 essays
The damage is the sharing; the forgery is the history
Two organs taken away, not one
1 generator
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mirror-lattice4 essays
The wrecked stem is the lattice it was cut from, wound the other way
What the wrecked orbit inherits
3 generators
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block-census2 essays
The block is one of the two numbers, and not always the smaller -
branch-stems1 essay
One rule, one rise, two branches that stay where they were put -
jugate-response1 essay
A bijugate stem answers in pairs, once the half turn is taken out
The sequence, averaged over blocks
2 generators
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stream-against-sequence2 essays
The wander is in the disturbance and not in what a plant lets you measure -
wander-curves5 essays
The disturbance with the largest wander leaves none in the sequence
Fractions with the same neighbours
1 generator
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matched-neighbourhood3 essays
Seven fractions with one neighbour distance and every denominator
The hop a cut leaves standing
1 generator
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hop-spectrum7 essays
One wrecked stem, lag by lag — golden, rise 0.005, organ 4 back
Two branches at one rise
1 generator
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response-on-both-branches3 essays
One rise, two seeds — the response of each
How many organs it takes
1 generator
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where-a-wreck-goes5 essays
Where a wrecked stem settles, whatever was taken from it
How deep the rule looks
1 generator
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what-the-ratio-hides5 essays
The wander climbs because its denominator falls
Which hop the rule keeps
1 generator
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hop-ladder7 essays
The hops of a 3/5 lattice, shortest first — golden, rise 0.026
A count with a factor in it
1 generator
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count-against-symmetry3 essays
Two patterns a counter cannot tell apart — counted 2/6 against 2/6
The rung below everything
1 generator
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coarse-ladder4 essays
Which rises are a lattice, from 0.04 to 0.13
The depth, in the wrong unit
2 generators
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corner-crossing3 essays
Which rule passes more drift — exponent 1.5 against exponent 3 -
depth-definitions3 essays
Four ways to count the rule's neighbourhood, and one ordering
One rung, swept
1 generator
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rung-geometry10 essays
The two contact steps change places inside the 5/8 rung
Whose neighbour was removed
1 generator
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lost-member-grid2 essays
The offsets where the removed organ belonged to one family
The corner, against the contact scale
1 generator
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corner-by-rise2 essays
The deeper rule against the disturbance's memory, at three contact scales
A finer rung, sampled finely
1 generator
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fine-ladder2 essays
The 3/5 rung at a tenth of the ladder's step
The band where two movers come apart
1 generator
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band-grid9 essays
A divergence that does not move across the 5/8 band
Where in its rung a stem was grown
1 generator
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position-column4 essays
The column the census never carried
The reference a wrecked stem does not have
1 generator
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displacement-profile2 essays
What a cut moves, organ by organ
A panel with no room to report
1 generator
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ceiling-shares2 essays
How many seeds the deeper rule takes, at three disturbances
How long a stem takes to settle
1 generator
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settle-times4 essays
How many organs a stem needs before it is on a lattice
Two rungs, one angle
1 generator
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angle-down-the-ladder5 essays
The settled divergence down the golden branch
Every handover, and the band around it
1 generator
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band-ordering5 essays
What each band holds, and what it moves
The shape of what a cut leaves behind
1 generator
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profile-levels8 essays
A period of 8, and the two classes that are not with the rest
Both walls of the slot
1 generator
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slot-design8 essays
Removing one wall of the slot, then the other, then both
The wall, against the falloff
1 generator
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exponent-table8 essays
How many starting angles reach a lattice, by rise and by falloff
One band, cut at every rise
1 generator
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band-at-full-resolution9 essays
Every rise of the 8/13 band, cut at every offset
Which two chains changed places
1 generator
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the-exchanged-pair7 essays
A period of 8, with the hole's own chain at the top
The slot interaction, across the ladder
1 generator
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interaction-across-the-ladder3 essays
The slot interaction at 30 lattices, gathered by rung
Every destination, counted
1 generator
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every-destination-counted6 essays
Every destination in the settling table, counted
The same cuts, run twice as far
1 generator
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profile-at-two-lengths5 essays
One cut's profile over 600 organs, with both onsets marked
The second band, cut whole
1 generator
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wrecking-across-a-band4 essays
Which offsets wreck across the Lucas 7/11 band
A fifth cluster, and the search for it
1 generator
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searching-the-fine-end5 essays
Twenty rises at the fine end of both branches, cut at every offset
The reading window, moved
1 generator
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spread-against-the-window3 essays
Each cut's class spread at three reading windows
Where a slot loses a wall
1 generator
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where-the-wall-goes3 essays
The golden 5/8 rung swept at 27 rises, with each removal's cost
Twenty starting angles
1 generator
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where-each-angle-goes6 essays
Where a stem started at each of twenty angles ends up, at a falloff exponent of 3
The rows the exchange set aside
1 generator
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excluded-rows5 essays
The 13 cuts the exchange sets aside, chain by chain
The third band, cut whole
1 generator
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three-bands-cut-whole4 essays
All three bands cut at every rise, offset by offset
Where the survivor changes on a rung
1 generator
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where-the-survivor-changes4 essays
The Lucas 7/11 rung between 0.007 and 0.006, cut at every rise
The common level, recomputed
1 generator
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where-the-level-sits4 essays
The eight rows where the two levels disagree
Where a wrecked run finishes
1 generator
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endpoints-against-destinations3 essays
Wrecked endpoints against the settling table's destinations
Forty starting angles
1 generator
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three-samplings4 essays
How often a stem settles, at three samplings of the starting angle
The angle a fork should make
1 generator
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fork-angle7 essays
The fork the cost chooses at a daughter ratio of 1: 37.47 and 37.47 degrees
Raup's boundary, computed
1 generator
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raup-boundary7 essays
The boundary located at 481 expansions, against D = 1/W
The wall, relocated
1 generator
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wall-relocated4 essays
The four walls at nine levels, 40 starting angles on the published rises
What an edge of a basin is
1 generator
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basin-edge4 essays
Six boundaries on three basins, five kinds between them, and three that are edges
The cells that are not hexagons
1 generator
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topological-charge4 essays
135 fives and 129 sevens among 1631 interior cells
What an error in the radii costs
1 generator
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exponent-error8 essays
A tree built at 3, measured to 2%, reads 2.957 on the informative band
The wrecked runs, regrown
1 generator
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regrown-run3 essays
Predicted 29 of 63 settle; 17 do
Recovering a growth factor
1 generator
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spiral-fit10 essays
Every assumed centre from 0.01 to 500 innermost radii, at 19 spans, against a spiral drawn at 3.2
The band at twice the resolution
1 generator
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finer-grid3 essays
19 changes and 2 at the coarse step, 21 and 2 at half of it
Two definitions of a neighbour
1 generator
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neighbour-definition5 essays
A cut-off would have to exceed 2.236 and not exceed 1.441, and nothing does both
The ladder, cut whole
1 generator
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ladder-cut-whole5 essays
The Lucas 4/7 cut whole, beside the three bands cut before it
The window a count is read over
1 generator
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read-window4 essays
All 19 destinations, counted at 17 windows from 20 to 800 organs
The rungs, walked at the grid
1 generator
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rung-walk3 essays
Six rungs walked at the grid, 10 crossings between them