Taking Fractals off the Page

To generate new images, more than 70 examples are included with the installation of Mandelbulber that you can use as starting points. Clicking on the button Load example pulls up a file dialog where you can load one of them. For example, you could load "menger sponge.fract". Clicking the render button will generate a 3-D Sierpinski sponge (Figure 4). Although technically, the set is only one topological dimension that encloses zero volume (aren't fractals weird?).

Figure 4. A Sierpinski sponge has infinite surface area and zero volume.

What can you change in Mandelbulber? Clicking on the fractal button pulls up the pane where you can set the parameters for the fractal itself (Figure 5). You can select from several different types of fractal formula types, such as mandelbulb, quaternion or menger sponge. You can set several options, depending on exactly which fractal type you choose. For example, if you select the iterated function system (IFS), you then can click on the IFS tab to set several different parameters.

Figure 5. There are several different fractal types from which to choose.

One of the issues is coming up with truly unique, yet aesthetically pleasing, sets of equations with which to experiment. To help in this regard, Mandelbulber has a hybrid option in the list of fractal types. When you select this option, you then can choose the hybrid button and set up to five different fractal equations (Figure 6). With this option, you can create very complex and sophisticated fractals to render.

Figure 6. You can create a hybrid system made from a mix of up to five different fractal types.

Mandelbulber doesn't just generate static images of these higher dimensional fractals. There is an option to generate animations of how these images change when some parameter is swept over. To start, you need to click on the Timeline button at the bottom of the view pane. This pulls up a timeline window where you can set the parameters used to generate your animation. The record button puts parameters into the actual keyframe number (Key no. field on the right). It then loads and renders the next keyframe if it is not the last keyframe.

Then, you can add new keyframes with the "insert after" button or delete keyframes with the Delete button. To modify a given keyframe, you can double-click it to set the parameters, and then you can click on record to render the keyframe.

Interpolation between the keyframes is handled by Catmull-Rom splines. Once you have the keyframes handled, you will need to render the full animation. Clicking on the Animation button in the main window brings up the parameters you can set. These include things like the number of frames to render from the keyframes, as well as the start and end frame numbers. You then can click on the Render from key-frames button to generate the animation. On my netbook, this is a pretty long process. For image generation, you also have control over camera position, lighting and shader options. You should be able to generate the exact image or animation that you want.

If you are looking to generate some amazing 3-D landscapes or unique shapes for something science-fictiony, you definitely should check out Mandelbulber—just be prepared to lose several hours as you start playing with all of the parameters available.

______________________

Joey Bernard has a background in both physics and computer science. This serves him well in his day job as a computational research consultant at the University of New Brunswick. He also teaches computational physics and parallel programming.

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Accessing your cars Work

sollen's picture

Accessing your cars Work Light heater core can be a challenge sometimes, but replacement is usually a simple matter of clamping off and removing hoses and the replacing the heater core itself.

In yet other cases,

sollen's picture

In yet other cases, mechanical parts work in conjunction with fluids. As such, special care needs to be taken. A good example of this is replacing parts in your cars Work Lights cooling system. Generally, replacing a water pump or radiator isn’t all that difficult.

Hungry

Brassica oleracea's picture

Looks like a Romanesco broccoli

C.H.O.A.S

Ridwaan Banoo's picture

Hi
I saw this funny looking thing while just scan-reading a Linux Journal page. It much reminded me of the branch of Mathematics that deals with 'chaos'. Like a beautiful world hidden inside another world.

I just wish I could experiment with this kind of math.... chaos and now 'fractals'. Where can I see more examples please tell!!

Thank you.

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