Photo Fractals

Christopher Nicolai | moc.scilednam@sirhc

Interactive color camera fractal. Tap, drag, pinch, and tilt to explore Mandelbrot and Julia sets. Use photos as source material for iterative conformal mapping. Realtime WebGL fractal photography on your phone's GPU. Make your own fractal photos free online.

See also: Michael Rule's Perceptron (Rapid Fractal Rendering with Conformal Mapping and Video Feedback)

Photo Fractals

This is a camera crossed with a fractal explorer (Mandelbrot and Julia sets).
Swirl the fractal with your finger, or using your phone's tilt sensor.
High-res prints available on request.

Basics

Press 📷 to choose a video source.
Press 🌈 to switch between image colors or color table rendering.
There are three rendering modes:
A: The pixel z0 = x + yi takes the average color of source pixels at z0, z1, z2, ..., zn.
B: The pixel zn = x + yi takes the average color of source pixels at zn, zn-1, zn-2, ..., z0. For each zi, there are two solutions for zi-1. We pick the one nearest to zi.
C: The image is first made into black and white, by thresholding or dithering. Then for each pixel z0 we find the escape iteration number by finding the first zi which is on a white pixel. We use that number as an index into the color table.

Touch

Press 🌀 then drag along the picture to change the fractal (Julia coordinate).
Press 🕂 to pan and pinch-zoom.

Gallery

Press # to browse saved pics, or upload your own to the shared gallery
Speed Dial pics are saved to your device, and not uploaded.

Tilt

Press 🏄 to control the picture by tilting your phone.
🏂 starts tilting; the slider controls sensitivity.
📲 lets you connect other tilting phones.
🌀 tilts the fractal (Julia coord).
tilts the source image offset.
recenters.

📠 High-res prints

Email @ for a download code.

🎨 Colors

In 🌈 mode A, B: adjusts brightness, hue, etc.
In 🌈 mode C: custom color table.
+, -: add or remove handles.
Pick a handle to adjust Position, Transition type, Hue, Saturation, and Value (brightness).
📌 saves as a favorite.

Fractal controls

🌌 returns to the full Mandelbrot set.
📷 clears the photo.

🌎 Map

Shows the Julia coordinate and zoom region.
█ zoom area
█ target Julia coord
█ actual Julia coord

🎡 Animation

Rhythmically varies the Julia coordinate.

Credits

Christopher Nicolai: camera concept, programming, UI design, remote sensors.
Benoit Mandelbrot: Julia set visualizations by escape iteration number (🌈 mode C).
Gaston Julia: discovered z = z2 + c.
Michael Rule: developed a similar fractal camera, which he described via conformal mapping

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📷
Christopher Nicolai mandelics.com
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email me for a code
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Tune your phone to mandelics.com/tilt#joker to join in