math.plot draws a curve from an equation. Use a standalone plot for curves in
drawing coordinates, or put plots inside math.plane when several series share
axes and data coordinates.
The language tour introduces both forms. This page concentrates on the sampler's reach and limits.
Every plot uses the same bounded expression language: eighteen functions,
pi, tau, e, arithmetic, and one independent variable. That is enough for
classical curves, damped waves, implicit contours, and finite series.
For example, a superformula needs no special constructor:
use "etchl/math" as math
diagram "Superformula" {
shape: math.plot {
at = (200, 200)
x = 110 * ((abs(cos(3*t/4))) ^ 8 + (abs(sin(3*t/4))) ^ 8) ^ -0.125 * cos(t)
y = 110 * ((abs(cos(3*t/4))) ^ 8 + (abs(sin(3*t/4))) ^ 8) ^ -0.125 * sin(t)
t in [0, tau]
stroke = "#16a34a"
}
}
The full gallery is in
examples/curve-gallery.etchl.
tolerance is the greatest permitted distance, in pixels, between a curve and
the line Etchl draws. The sampler proves a bound for each span with interval
arithmetic. If it cannot prove the requested tolerance within the point budget,
compilation fails instead of returning an unchecked approximation.
The property tests compare drawn segments with their source equations and exercise high-frequency curves, poles, discontinuities, and budget boundaries.
A finite Weierstrass series is an ordinary function of one variable, so it fits the plotting model even as higher terms add finer oscillations.
The same applies to other finite series:
Iterated systems such as Koch, Sierpinski, Mandelbrot, and Julia constructions
do not fit math.plot. They require iteration or complex state, neither of
which belongs to the expression language. They should be expressed through a
purpose-built abstraction, not hidden inside general expressions.
Interval arithmetic treats repeated occurrences of a variable independently. Equivalent expressions can therefore differ in how tightly they can be bounded:
abs(u - round(u))
abs(asin(sin(pi * u))) / pi
Both compute distance to the nearest integer. The second form bounds tightly;
the first may be rejected because the sampler cannot prove that the two uses of
u move together. Rewriting an equation can help when increasing tolerance
would lose too much detail.
A plot is rejected when it exceeds any of these safeguards:
- 5,000 drawn points;
- 512 expression terms or 64 nested expression levels;
- the freehand coordinate-magnitude limit;
- a finite interval proof, including poles and unbounded values.
A coarser tolerance is usually the right response to the point limit. Larger or structurally different computations belong in a dedicated constructor.
A plot can be styled, connected, measured with along(...), or mixed with
ordinary nodes.
See examples/plot-flow.etchl for the complete
source. The normative grammar and limits are in the
language specification.