Fractals are mathematical figures, based on fairly simple mathematical formulas. Infinite repetition produces intricate structures that look beautiful. We present to you some iPad apps that allow you to conjure up these beautiful figures on your screen.
The masses were introduced to the fractal in the 1990s, thanks in part to the MS-DOS program Fractint that appeared in the late 1980s. You can still run it in, for example, DosBox. And just like then, the pictures are still beautiful. Fast forward to now, where multicore CPUs with integrated FPU (arithmetic processor) and adjacent GPUs no longer turn around for heavy calculations, not even on a mobile phone.
It makes an app like Frax calculates complex fractals in real-time, on which you can zoom in and out in just as real-time. In fact, the standard resolution of the average iPad is more than sufficient for making sharp A4 prints. But if you want the case to render in a higher resolution, you can do that on your device itself by upgrading to the Pro version for a few euros. Or buy a handful of ‘render credits’ to have the case render in the cloud in much higher resolutions for printing at football field size.
For most people, however, playing with the various fractals, settings and more will be the most fun. It is also possible to record videos, so that you can use the generated fractals – as an image or moving – in other creative projects. Recommended!
Final Fractal
Final Fractal is slightly less ‘eye candy’ in terms of smooth movements than Frax. On the other hand, you buy the full version with all features for € 0.99, so that’s very manageable. You can also effortlessly render hires images on your device, up to 28 megapixels to be exact. That is more than enough for even large format printing.
However, the images are only saved in .jpg format. No drama in itself, but also saving as .png for example would have been nice for purists who want to continue working in a photo editor without any loss of quality. Although the images may be a bit too large for the average iPad, in terms of storage space.
A nice detail of Final Fractal is that after zooming in, rotating, coloring and more you can export your image as a QR code and share it easily and quickly with someone who also has this app installed. It immediately shows the power of fractals: no matter how complex the image is, it is and remains a simple mathematical formula that can easily be stored in a QR code.
Once you’ve discovered a beautiful point in a fractal and zoomed in on it, you can also see an animation – flowing silky smooth in real-time – of the fully visible fractal zooming in on ‘your’ particle.
Mandelbulb
The app proves that fractals don’t have to be ‘flat’ at all Mandelbulb†Herein, a 3D representation of the well-known Mandelbrot fractal built up. You can tweak the ‘blob’ via the settings menu (cogwheel at the top left). We advise you to enable the anti-aliasing option by default.
Most iPads and iPhones of more recent date do not turn their hand around for this. Experiment with the different environments available. If you have found a nice viewing point, the blob can be exported in high resolution; again via the settings gear.
Fractal Way
Of Fractal Way you can explore the world of the Julia and Mandelbrot fractals. The basic version of the app is free, but if you want unlimited zooming (which is nice in a fractal), you have to pay €4.99 via an in-app purchase. We find the price of €24.99 a bit exaggerated to be able to export to custom resolutions.
If you want that, you’ll be a lot cheaper with the other apps from this article. For the rest it works perfectly fine. Choose from the Julia or Mandelbrot set by pressing the J or M button. You can also put them next to each other by clicking on the J button containing the wrench. Rendering is smooth, but there’s no such thing as quick ‘smooth’ zooming and scrolling through the fractals.
There is, however, a library of predefined fractals available; tap the button with the ‘film strip’ in the top right corner. Stay further away from the export button, before you know it you will pay the aforementioned €24.99. If you use an iPad, a screenshot is also fine, even for printing. In short: a nice app, but a shame about that expensive export function.
in the cloud
There are also various fractal generators online that simply run in the browser. One nice one is this one†Here you can clearly see that even with very simple basic shapes (lines) the most complex figures are quickly created. By playing with the buttons at the bottom of the screen, you can quickly see what exactly is going on. The same basic principle is also applied to the much more complex (looking) fractals, but all kinds of extra tricks such as tessellation, lighting angle, 3D effects and more are pulled out of the closet.
In essence, those fractals below the line are also built up from simple geometric repetitions. An example of such a more embellished Fractal generator find you here, where you can play with the classic Mandelbrot set. It is practical that a few things are also explained in terms of underlying mathematics. This way you can nicely compare theory and practice!
If you have a taste for fractals, you can see the different basic types here†And not just see, because they are interactive and are calculated in your browser. And again with an explanation. For example, we learn that the ‘Pythagoras Tree’ was invented by the Dutch math teacher Albert E. Bosman, back in 1942.
And well, that’s exactly what makes a fractal dangerous: once you’re ‘addicted’ to it, it’s hard to get rid of it. Fortunately, it is a fairly harmless addiction. Finally, a tip: fractals are also great as backgrounds for your phone or desktop!
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