Fractal Generator
Fractals are mathematics as art. Though they are purely mathematical in character, fractals draw us in with their otherworldly beauty, with their ripples, ridges and loops. Eye-catching. Our Fractal Generator tool allows you to explore five of the most common fractal sets.
A fractal is not drawn. It is calculated. A mathematician takes a simple equation and maps it in 2D or 3D. What emerges from it is the shape of infinity, self-similar at every scale, laced with spirals and loops, filiments, never repeating exactly and never ends. When you zoom down, you do not meet a point where repetition of structure ends; you do not reach a resolution limit. The detail continues. Spirals appear inside spirals and repeat within spirals. A year of zooming and you still would not meet the end. On the computer or mobile screen we are limited by resolution or processing power, but in the mathematical world it never ends.
The mathematician Benoit Mandelbrot, who worked extensively with fractals and coined the word fractal in 1975, likened fractals to “the geometry of nature,” or the character of “rough.” The branching of rivers, the meanders of coastlines, and a lightning bolt follow fractal like rules, thought they cap at physical limits.
drag to pan
right-click zooms out
tap to zoom in · double-tap out
Triangle to Select
How to use Fractal World
Our Fractal World tool lets you explore five fractal families. All are based on a mathematical equation in recursive form. For this tool we have Mandelbrot, Julia, Burning Ship, Tricorn, and Cubic Z3.
Use your mouse wheel to zoom toward or away from the cursor position. The tool zooms into exactly where you are pointing. Click and drag to pan across the plane. Right-click anywhere to zoom out by half. On a touch device, pinch to zoom and drag with one finger to pan.
The heads-up display in the upper left shows your current center coordinates in the complex plane and your zoom level relative to the default view. As you zoom deeper, the coordinate display updates in real time so you can record interesting locations.
Palettes
The six palettes were defined by graphics researcher Inigo Quilez. Each is a smooth cosine gradient so there are no hard edges.
Iterations
The slider sets the maximum number of iterations a point is tested for before it is treated as bounded and given the a color. Points that escape are stopped. The default of 300 is a good balance.
Flow mode
Flow animates color cycles across the fractal. Flow works on any fractal type. Press F or click the Flow button to toggle it. Press it again to stop.
Saving your work
Click Save PNG or press S to download the current view at full canvas resolution. The file is named with a timestamp so future saves do not overwrite each other. For high-resolution saves, expand your browser to full screen before saving.
Keyboard shortcuts
Click the canvas first to give it focus, then: R resets the view to the default position and zoom. F toggles Flow animation. S saves the current frame as a PNG.
Frequently asked questions
What is a fractal?
A fractal is a figure that has a similar shape up and down the scale. It is computed mathematically and usually involves iterative computations.
What are the Re and Im boxes?
Our fractal canvas is made of pixels, and each pixel is not just a pixel but a location in a defined universe. It is a fractal world, and every location in it is calculated by the one math law we choose. The Re and Im sliders on the Julia set fractal let you choose the constant, the one number every pixel on the screen is calculated against. Re moves that number left and right, Im moves it up and down. The math is the same, but the calculated figure and how it bends on the paper are different.
Why do fractals iterate forever?
It is never possible to reach the end of a fractal shape because zooming into any edge reveals the same complexity repeating; there is always more structure to find. Unlike natural fractals, which stop at the physical limit, a mathematical fractal has no smallest scale; it divides and recurses forever.
Can I use images saved from Fractal World in my own work?
Images made with our tool are yours. Use your renders freely for personal projects, art, writing, social media, or education. Attribution to GoRhyme is appreciated but not required.