| A trip in the fractional dimension(09-08-2025) Chaos is a very interesting field of study, as it is at the frontier between natural sciences, mathematics and arts. Indeed chaotic behaviors can appear in many systems relevant to chemistry, be it in computational simulations or in reactions thermal control. But it allows also to generate beautiful pictures of many sorts... A small introduction on chaos is provided here, wih emphasis on the concept of fractional dimension which is the common factor for most so called "fractal... |
Dynamic clouds(09-08-2025) A pretty cool javascript to draw fractal clouds. Try it on the fly! A class of fractal, the "folded plan" is used to make clouds. A plan is of dimension 2. When it is folded like aluminium foils, its dimension increase between 2 and 3. Hence such objects are fractals. With adequate coloring, such folded plans can be used to create rather realistic landscapes, for instance by adding a cut-off value for the sea level. Similarly, looking at the plan from above and using the alt... |
| Fractal Software (04-01-2012) CSE Fractals III
All fractal images on this website have been created with the Malab program CSE Fractals III written by L.Cavin. This program can be downloaded here for free. This is a program for Matlab - you will require a running Matlab to start this software! Features and Usage Call fractal_explore... |
Lindenmayer systems(09-08-2025) A cool javascript to let you play with Lindenmayer String Systems... Lindenmayer Systems Presets: Demo... Koch Island Migrating Island Square Madness |
| Fractal Landscape(26-04-2025)
Fractal Landscape Grid
Scrolling through a procedurally generated landscape.
Your browser does not support Canvas.
Based on an initial grid script, modified with Diamond-Square terrain and perspective projection. (Click canvas to toggle animation)
Folded Plan Fractals and Their Dimension
What is a Folded Plan Fractal? A fol... |
3D Attractors(10-08-2025)
Explore the fascinating world of 3D strange attractors, a cornerstone of chaos theory.
This interactive demonstration reveals how simple sets of mathematical equations can generate infinitely complex and beautiful patterns.
Use the menu below to select different chaotic systems and watch their intricate structures unfold in real-time.
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| Map Explorer(10-08-2025) The intricate beauty of 2D strange attractors, generated by applying a simple set of equations to a single point, millions of times over. Despite the deterministic nature of these rules, the resulting patterns exhibit profound chaotic behavior, forming complex and often beautiful fractal structures. Use the controls to select different mathematical systems and adjust their parameters to discover the infinite variety of shapes hidden within the chaos.
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Logistic Equation(10-08-2025) Explore the fascinating "road to chaos" through bifurcation diagrams. This visualization plots the long-term behavior of a simple iterated equation as a single parameter is varied along the horizontal axis. Watch as stable, predictable systems suddenly split (or bifurcate) into oscillating patterns, which in turn split again ever more rapidly, ultimately dissolving into the beautiful complexity of chaos.
The pattern of period-doubling is quantitatively the same for a very large class of the... |
| Newton Bassins(11-08-2025)
Controls
Click and drag to move. Use mouse wheel to zoom. Select Equation: |
Mandelbrot(11-08-2025)
Mandelbrot defined a new mapping of the complex plan (the Mandelbrot Set) by including all complex points that do not diverge to infinity when iteratively squared and added to the initial point: zi+1 = zi2 + z0. The boundary of the surface thus defined has the peculiar property of h... |
| Fractals Interactive Tools(12-08-2025)
An Introduction to Chaos and Fractals
Chaos theory is a fascinating field at the frontier of science, mathematics, and art. It reveals a hidden order in systems that appear random but are, in fact, deterministic. From the intricate patterns in nature to complex engineering problems, chaos provides a new lens through which to understand the world. This page offers a simple, illustrated tour of its core concepts.
The Logi... |
Quaternions(15-08-2025)
Rendering Picture... This can take a few minutes. Con... |
| Landscapes(15-08-2025)
Controls
Scale 50
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Fractal Art (05-12-2008) |
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