The Unravelling of the Real 3D Mandelbrot Fractal. Visit First page Experimenting with iterations and powers Okay enough eye candy for now.
Let's have a closer look at the structure of this beast. Firstly, the old 2D Mandelbrot can be represented as an evolution of iterations. At iteration 1, it's merely a circle, so we'll start from iteration 2. The final stage (infinity iterations) is very similar at first glance to iteration 5000 (unless you zoom right in), as the shape converges to a shape comprised of tangent circles.
One interesting question is: Does this same phenomenon happen with our power 8, 3D Mandelbulb? Power 8 (zooming into this object produces all the eye candy on the previous page): Click any picture to enlarge. A higher quality image below, and a super-large 4000x4000 version is here for the patient. And once you zoom into that, you get the magic as shown before. Squaring (power 2) Finally, let's take a look at power 3.
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" "by far i think it is the only program which can do heightmap rendering easily" "a most excellent software" Untitled. Inner view of the Mandelbox. Mandelbox. Software 3D graphics - index. Softology's Channel True 3D mandelbrot type fractal. Anyway after playing with the options for the 3D version I settled on this: r i jr r i ji i -r -jj j -j -r What is this table called and how do I find the squaring function from this table?
It's just one possible 3D unit vector multiplication table i.e. in this case the multiplications are commutative and: real*real -> real, real*imag -> imag, imag*imag -> -real, real*jmag -> jmag, imag*jmag -> -jmag and jmag*jmag -> -real. For the squaring function we want: Welcome to Fractal Forums - Index. Mystery of the Real 3D Mandelbrot Fractal. They're all very nice, but imagine such pictures in three dimensions, with all the advantages that 3D can allow such as parallax, perspective, and richer detail along with subtle light sourcing, shadows, and reflections.
And actually, it turns out there are quite a few '3D' Mandelbot pics out there if you look..... Mandelbrot Flavours .....But are they the real McCoy, or just pale imitations? In fact, whenever you see a so-called 3D Mandelbrot image, roughly speaking, they can be divided into four types: Existence of 3D Mandelbrot set? No, the thing I've been looking for has the essential characteristics of the traditional 2D Mandelbrot, but extended to 3 dimensions. We can try and guess the overall shape's outline too. Below is a third visualization using a formula I created based on pseudo 3 dimensional complex numbers (and nicely rendered by Thomas Ludwig). Also see Thomas' amazing metallic render of the same design. Search as long as you like. Let's take that last quote. External links: Hypercomplex Fractals. Here is a 4th order inverse Juliabulb set with 600 million spheres.
The triplex raised to the 4th power has 16 unique valid roots. Garth Thornton was the first person to point out that, in general, the triplex raised to the nth power has n2 unique valid roots. I posted a formula for all integer powers here.