We know and study them in standard mathematics and Euclidean geometry in the idealised forms of straight lines, triangles, circles, 3D polygons etc that we all know from elementary math and school. Mandelbrot at the time and throughout his scientific career studied with new mathematical methods the "roughness" and real, non "smooth" and non idealised shapes and contours of real life objects of nature such as everyday rough surfaces of objects (like the barks of trees), boarders and coastlines of countries and islands, the shape of mountain ridges, the formation of river beds and river deltas, all sorts of plants and flowers and even the shape of graphs representing the fluctuations of stock prices.Ĭontrary to most mathematicians of his time he did not see these shapes and forms as mishaps of nature or bad quality versions of "ideal" perfect shapes like the Platonists since Plato do. With these books Mandelbrot laid the foundations for the new mathematical science of Fractal Geometry. His first popular science book about fractals was published in English in 1977 and called "Fractals: Form, Chance and Dimension" and his second and most popular book - and still worth and a recommended reading today - was called "The Fractal Geometry of Nature" published in 1982. I nevertheless hope you enjoy the read - maybe on a rainy day when you have nothing better to do -)įractals can be found pretty much everywhere in nature ! However, fractals as we know and study them today have only become noticed and popular with the general public after the publication of two books by the Polish mathematical genius Benoit Mandelbrot (1924 - 2010 see picture below) who first used and introduced the term "fractals". Even though I cover a lot of ground and topics, the content must remain a bit superficial as some of the underlying scientific background and theories would be very complex and too difficult to explain here. Please note: this is an introductory and overview article. The second part will focus more on fractal processes (rather than spatial fractal structures), fractal time- series, fractals and computational complexity and a further fractal analysis of our brains, language, music, oscillations and resonance, our perception and our thinking processes. I will published the second part of this article early next week. In this first part here I explain the basic concepts and give plenty of examples of fractals as they can be found and are studied in mathematics, physics, complex systems, chaos theory, quantum theory, nature in general, in the arts, in evolution theory and (molecular and quantum) biology and especially in our bodies and brains. I have split the article in two parts because of the length and the time it would take to read the whole article at once. The screen shot will be in your photo album.This is the first part of two popular science overview articles I have written about fractals. Create a screen shot by pressing the sleep button on the top and home button at the same time. If you have red-cyan glasses available, you can see the fractal with real depth by enabling stereo mode.Ī one finger drag rotates the camera around the object, a two finger pinch is used for zooming and a three finger drag translates the camera. The accuracy of the fractal surface can also be set here.
The Settings tab also allows to enable an environment that is mirrored on the Mandelbulb fractal. You can also set these constant in the Settings tab. This app uses the GPU of the iPad to compute a 3D image of the fractal by ray tracing using OpenGL ES 2.0 shaders.ĭouble/Triple tap and drag the finger horizontally or vertically to change the shape of the Mandelbulb fractal. The Mandelbulb fractal is a 3-dimensional analog of the Mandelbrot set using an hypercomplex algebra based on spherical coordinates. Zooming makes an unlimited amount of detail visible.įractals are self-similar mathematical shapes in complex space. It renders the Mandelbulb fractal with high accuracy. Mandelbulb Raytracer is an exciting real-time ray tracer for the iPad. You can make the sculpture shiny by selecting an environment that will be reflected on the object.
Play with the parameters to create an unlimited number of exciting 3D shapes. Then use it as a background image to impress your friends. Be a virtual sculptor and create your own personal art in just seconds.
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