Mathematical Art Generator

What the preview computes while you move sliders

Each mode maps numbers to pixels in a different way. The shared idea is simple: sample a formula many times, push the results through color rules, then paint.

Parametric weave draws curves where both x and y depend on a running parameter t. You see several layers at once because density raises the frequency multipliers inside the sine and cosine products. Polar roses use angle θ and radius r(θ), then convert to Cartesian points around the center. Escape-time fill treats each pixel as a starting point in the complex plane and counts how long a quadratic iteration stays bounded before coloring the pixel. Branching tree grows a fractal-like structure by recursive line segments with shrinking length. Wave stack overlays sinusoids with different frequencies and offsets so peaks and troughs interfere.

Symmetry modes repeat or flip the stroke layer. Six-fold radial rotates the same stroke six times around the canvas center. Mirror reflects across a vertical axis through the center. Four-fold turn repeats with quarter rotations. Escape-time mode ignores symmetry today because the fill is computed per pixel in screen space. We kept the control visible so switching modes does not surprise you with a hidden reset.

If you want labeled axes, precise domains, or exported vector data, treat this page as a sketchpad and move to a dedicated plotter. The Parametric Equation Plotter is a better fit when you need readable scales. For polar conversions before you invent your own r(θ), open the Polar Coordinate Converter. For single-function graphs with numeric readouts, the Mathematical Function Grapher stays closer to coursework expectations.

Export sizing you should expect

Download writes the pixel grid you see after the last resize. On a phone held upright the square often lands between 320 and 400 CSS pixels wide. On a wide monitor it grows toward 720 pixels unless you shrink the window. Device pixel ratio scaling multiplies the internal buffer so edges stay sharper on high-density screens, but the PNG dimensions still match the CSS square you preview.

Need a 4K texture? Upscale in an image editor instead of expecting this page to allocate a multi-megapixel buffer. The studio favors responsive speed over archival resolution, which keeps redraws tolerable while you drag sliders.

Rose curves without the homework flashcards

A rose in polar form often shows up as r = cos(kθ) or r = sin(kθ). The preset labeled Rose jumps you into polar mode with a moderate density so petal counts change quickly as you drag. Cardioid-like shapes appear when you lower density and stay in polar mode. None of these presets claim textbook accuracy. They are starting coordinates for play.

When the canvas looks muddy or too busy

Escape-time fills cost more CPU than strokes because every pixel runs an inner loop. On phones the preview may stutter if density sits above fifteen. Branching depth is capped internally so recursion does not freeze the tab, which means very high density does not keep deepening the tree forever. Complex palettes map iteration counts to RGB with a small set of rules. They are not scientifically calibrated Julia sets.

Thin lines alias on dark backgrounds. If you need print-ready output, export PNG and trace or upscale in a vector tool. Colors are chosen for contrast on screen, not for color-blind simulation or print gamut.

Parametric weave

Layers of sin-cos products with independent frequency multipliers. Symmetry repeats each finished layer.

Polar roses

Radius modulates with cos(kθ/2) samples, traced over several turns. Good entry point for petal-like motifs.

Escape-time fill

Per-pixel iteration count from z ← z² + c style update with c tied to pixel position. Symmetry select does not alter this pass.

Branching tree

Recursive forks with hue from depth. Radial symmetry rotates the whole tree. Depth is limited for responsiveness.

Wave stack

Multiple sine waves across width with phase offsets. Mirror symmetry duplicates horizontally.

Where quick plots like this earn their keep

Motion designers sometimes need a looping still for a background plate. Teachers sometimes want a memorable image after a lesson on superposition. Hobbyists prototyping laser-cut panels use screenshots as first drafts before redrawing in CAD. In each case the goal is fast feedback, not publication-grade proof.

Shuffle settings exists for happy accidents. If you dislike random jumps, ignore it and move one slider at a time. Redraw recomputes with the same numbers, useful after a resize on mobile when the canvas rescales to the new width.

Mode snapshot

We recommend keeping one mode per session when you present to students. Jumping modes mid-sentence splits attention between geometry stories. If you need spiral-only control with polar families spelled out, the Spiral Generator offers a tighter focus than this broader studio.