CTO at Tough Tongue AI  ·  Self-hoster · IoT tinkerer · 3D printer · Hacker

I build for the long-running self-hosted shop — hardware that hums in a closet, software that doesn't need babysitting, small tools that compose well.

At Tough Tongue AI we're building a platform for building and orchestrating voice AI agents — multimodal, agentic, white-label ready. Try it →

• 💞 Looking to collaborate on self-hosted products.
• 📫 dsculptor@altmails.com

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." — Benoît Mandelbrot, The Fractal Geometry of Nature (1982)

_{Every image on this page is rendered by the Python package in this repo. A GitHub Action re-runs uv run build-all on every push — change a kernel, push, watch the profile redraw itself. Clone & run it →}

I have a conviction that great codebases are beautiful fractals.

A webpage is laid out as cards with rhythm and spacing. Each card is itself a smaller composition with its own rhythm and spacing. Zoom in further and you reach glyph rasterization — vectors arranged into letters, the same exercise repeating at a finer grain. Every level looks like the last, just smaller.

The same self-similarity hides everywhere:

• APIs built on top of APIs.
• Compilers that bootstrap themselves; new features echo old ones.
• Linux — a sprawling fractal of packages assembling smaller packages.
• Networking — layering as a textbook self-similar stack.
• A GET request → motherboard firmware — bits being munged at every scale.
• Neural networks — repeating layers stacked into deeper layers.

Build software the same way: pick a clean atom, then echo it.

History · Definition · Algorithms · Gallery · In the wild · Source

Long before they had a name, fractals were lurking on the edges of mainstream math — uncomfortable curves that respectable mathematicians wished would go away.

Mandelbrot resisted a single definition — fractals are a family, not a club with a bouncer. But three properties recur:

1. Self-similarity — zoom in; the whole pattern reappears at smaller scale.
2. Detail at every scale — there is no "smooth enough." Structure persists indefinitely.
3. Non-integer Hausdorff dimension — rougher than a line, less filling than a plane.

For a self-similar set of N copies each scaled by 1/r, the dimension is log(N) / log(r):

Non-integers sitting between integers — and that is the whole point.

Almost every famous fractal falls into one of three algorithmic families. This repo ships one renderer for each.

1. Escape-time — iterate z ← f(z, c) per pixel; ask how fast |z| runs to infinity. Points that don't escape form the fractal; the rest are colored by how fast. → Mandelbrot, Julia, Burning Ship.

2. Iterated Function Systems (chaos game) — pick a weighted affine map at random, apply it, plot, repeat 10⁵–10⁶ times. The attractor emerges from the noise as if it were always there. → Sierpinski triangle, Barnsley fern.

3. L-systems — start with a string, replace every character by a longer string, walk the result with a turtle. Born in a botany lab; now powers the foliage in every video game on Earth. → Koch snowflake, recursive tree.

Click any image for the full-resolution render.

Mandelbrot set  · 1980 z ← z² + c, starting from z₀ = 0 boundary dim = 2 (Shishikura, 1991) The most famous fractal, and one of the youngest. Take every complex c; iterate; the points whose orbit stays bounded are the black body. Described by Julia & Fatou in 1918 without ever being drawn — only seen by Mandelbrot in 1980 when computers had finally caught up.	Julia set  · 1918 z ← z² + c, c fixed = −0.7 + 0.27015i Fix a single c and ask the same question. Every Julia set is one vertical slice of the bigger story the Mandelbrot set tells. A Julia set is connected iff its c sits inside the Mandelbrot set. Pass any seed to uv run fractals julia -c … and watch it morph.
Burning Ship  · Michelitsch & Rössler, 1992 z ← (|Re z| + i·|Im z|)² + c The Mandelbrot iteration with absolute values slipped in. The map is no longer analytic, so smooth bulbs become hard angles, antennas, and silhouettes that look like ships ablaze on a sea of plasma.	Newton fractal  · z³ − 1 z ← z − f(z)/f′(z) Run Newton's method from every pixel; color by which root it converges to. The three primary basins are simple — but their boundary is fractal. Every two basins meet only where the third also lives. Cayley posed this in 1879 and got stuck.
Sierpinski triangle  · 1915 3 half-scale affine maps · dim = log 3 / log 2 ≈ 1.585 The chaos game in its purest form: pick a vertex of a triangle at random, jump halfway towards it, plot the point, repeat. After 300k jumps the Sierpinski triangle emerges from the noise as if it were always there.	Barnsley fern  · 1988 4 affine maps · weights {0.01, 0.85, 0.07, 0.07} A real fern's structure is encoded in four affine transformations. Run the chaos game with those weights and 500k points, and the fern appears. The inverse problem — finding the IFS for any image — kicked off fractal image compression.
Koch snowflake  · 1904 F → F+F--F+F, 60° · dim ≈ 1.262 The original "monster curve." Finite area, infinite non-differentiable perimeter. Each iteration replaces every segment with four shorter ones. The limit has no tangent anywhere — exactly the kind of object 19th-century mathematicians had hoped didn't exist.	Recursive tree  · L-system F → FF+[+F-F-F]-[-F+F+F], 22.5° An L-system rewrites a string; a turtle walks the result. The brackets push and pop state — they're how a 1D string grows branches. Lindenmayer invented the formalism in 1968 to model seaweed. The same trick now powers the foliage in every video game on Earth.

Fractals are not a curiosity. They are the geometry the world actually uses when smoothness gets in the way.

Once you've seen the trick, you can't unsee it. The world is rough at every scale — smoothness is the exception.

_{If you read this far — tell me which fractal is your favorite.}