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Julia Set Image Transformer
This interactive visualization transforms your images using the mathematics of Julia sets, creating beautiful fractal patterns from your photos.
What are Julia Sets?
Julia sets are fractals that emerge from a simple mathematical iteration in the complex plane. For each point z in the complex plane, we repeatedly apply the function:
z ← z² + c
Where c is a constant complex number. Depending on the value of c, different fractal patterns emerge.
How This Works
When you upload an image, each pixel on the screen goes through this process:
- The pixel's position is converted to a complex number z
- We iterate the formula z ← z² + c multiple times
- If z stays within a bounded region (doesn't "escape"), we color that pixel on the screen according to where it ends up on your image
Interacting with the Visualization
You can:
- Change the fractal pattern by clicking and dragging on the canvas to set different values of c
- Zoom in/out using the mouse wheel to explore the fractal at different scales
- Pan around by holding the space key while dragging
- Reset to return to the initial settings
About the Mathematics
Julia sets are closely related to the famous Mandelbrot set. While the Mandelbrot set shows which values of c create bounded Julia sets, each individual Julia set is created by fixing a specific value of c and testing which points in the complex plane remain bounded under iteration.
This visualization combines the mathematical beauty of Julia sets with your own images to create unique artistic renderings.