RootSquare · open-source logo generation

RootSquare’s radical window

The RootSquare logo reflects our philosophy. The warped field is the inevitably noisy environments we find ourselves in: sometimes noisy data, sometimes noisy AI slop, sometimes noisy models. The square root symbolizes our goal: becoming an aperture through which noise is silenced and order becomes visible. The lines inside the window are the same as the ones outside, just organized. Now, the tool that draws our marks is below, and it is yours to play with. Source and licence on GitHub

Parameters

Export

Background

Image scale

Video height

Video format

File name

Copy SVG puts the vector straight on your clipboard, ready to paste into Figma, Illustrator or Inkscape. Every file you save is written alongside a text file of the same name holding the parameters that made it. If you paste that back into the box below and press Apply, you get the identical picture.

The JSON is editable: change a value or paste a whole saved set and press Apply (or Cmd/Ctrl+Enter). Values are clamped to each control's range, and any unrecognized values are ignored, with a count shown. These are the same values as the CONFIG object at the top of this file's script; edit them there to change the defaults permanently. The damping band is measured inwards from the window's edge: widen it past the cut-out's clearance and the wobble starts leaking into the window.

How our logo is built

Every mesh point is pushed off its lattice position by the slope of a height field, and that field is a sum of plane waves running in randomly chosen directions:

h(x, y, t) = Σ_i a_i sin(k_i(x cos θ_i + y sin θ_i) + ω_it + φ_i)

displacement = A · ∇h · damp(x, y)

damp = 0 inside the window, 1 outside

Each symbol is a control in the panel:

k_i = 2πn_i/λ: how tight the ripple is Base wavelength
a_i = 1/n_i^p: how much that mode contributes Amplitude falloff
θ_i: its heading, random Seed
ω_i ∝ n_i/T: how fast it drifts Drift period
i: one term per wave Wave count
A: the overall push, in pixels Warp amplitude
damp: 1 in open field, 0 where order holds Window + Damping band

h itself is never evaluated. Only its gradient is, because differentiating the sine leaves a cosine with the direction cosines folded in, so each mode costs two constants and one cosine per sample. The surface is a fiction; what you see is its slope.

damp is a blend weight rather than a multiplier: the displacement runs between the full field value and a target. In Rest that target is zero, which is the product shown above. Keep offset and Local mean use non-zero targets, which is why a straightened line can still sit off its lattice position. The noise is removed; the signal is not replaced.

Randomizing each wave's heading is what removes the diagonal: with every mode running along the same two axes, the crests line up into a traveling plaid, whereas incommensurate headings and drift rates never resolve to a single direction. Amplitude falls off as 1/n^1.6, which keeps the long wavelengths dominant and holds the sheet's stretch short of the point where it folds back through itself. At the defaults the margin is about a factor of two; push both the wave count and the warp amplitude to the tops of their ranges and the field can crease.