Draw Special Functions
Blancmange, Weierstrass, Minkowski, Thomae, Dirichlet. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Draw Special Functions
- 1. Pick a function to plot. Choose Blancmange (Takagi) curve, Weierstrass function, Minkowski question mark, Thomae's function or Dirichlet function from the Function setting, each illustrating a different kind of mathematical pathology.
- 2. Adjust the canvas and styling. Set Width and Height for the plot, and choose Line color and Background color along with Line width to control the appearance of the curve.
- 3. Review the rendered plot. The tool draws the selected function's graph as an SVG, showing its characteristic self-similar, fractal-like, or discontinuous structure across the plotted range.
- 4. Download the image. Save the rendered plot to illustrate a real analysis lecture, a blog post on pathological functions, or a discussion of continuity and differentiability.
When to use Draw Special Functions
Draw Special Functions plots five famous pathological functions from real analysis, chosen for properties that defy everyday intuition, like being continuous everywhere yet differentiable nowhere. Use it wherever these functions need a visual.
- Illustrating continuity without differentiability. A real analysis course introduces the Weierstrass function as the classic example of a function continuous everywhere but differentiable nowhere, and a plotted image makes the jagged self-similarity visible.
- Explaining Thomae's popcorn function. You are writing about functions continuous at irrationals but discontinuous at rationals, and rendering Thomae's function shows the characteristic spikes at rational points along the axis.
- Adding a visual to a pathological functions blog post. An article surveying strange functions in analysis, like the blancmange curve or the Minkowski question mark function, needs rendered images for each one discussed.
- Comparing fractal-like curves side by side. You want to render the Blancmange curve and the Weierstrass function at the same size to compare their self-similar structure for a presentation on fractal geometry.
Examples
The blancmange curve
Output
An SVG plot of the Takagi function, continuous everywhere but differentiable nowhere.
The Dirichlet function
Output
An illustrative scatter of the nowhere-continuous indicator of the rationals: sample rationals at y = 1, a dense sample of the y = 0 line for the irrationals. The true function cannot be drawn point-for-point.
About the Draw Special Functions tool
Draw Special Functions runs as plain JavaScript in your browser tab, with no server behind it. Blancmange, Weierstrass, Minkowski, Thomae, Dirichlet. Whatever you put in stays on your device from start to finish.
The tool is part of EditSafely's Math Tools section, 234 single-purpose utilities built around the same idea: open the page, get the result, keep your data to yourself.
You can shape the output with 6 settings, including Function, Width (px), Height (px) and Line color, and the result refreshes the moment you change one. 2 worked examples further down the page show exactly what the tool produces for real inputs.
That local-first design has practical benefits beyond privacy. The tool keeps working on a flaky connection once the page has loaded, results are instant because nothing round-trips to a server, and it is safe to use with confidential material.
Frequently asked questions
Is Draw Special Functions free to use?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
Everything happens locally. Your browser downloads the tool's code once, then does all the processing itself; nothing you enter is transmitted, stored or logged. You can even go offline after the page loads and it will still work.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
No. The tool works in any modern browser on desktop, tablet or phone. There is no account to create, no extension to add and no software to install.
Can I save what the tool produces?
Yes. Use the download or copy controls in the output panel to keep the rendered result once it looks the way you want.