computer science

XaoS

XaoS is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand XaoS rather than just read about it. In short: XaoS is an interactive fractal zoomer program. It allows the user to continuously zoom in or out of a fractal in real-time.

Key takeaways

XaoS belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect XaoS to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of XaoS from memory before moving on to harder problems.

Reference excerpt

XaoS is an interactive fractal zoomer program. It allows the user to continuously zoom in or out of a fractal in real-time. XaoS is licensed under GPL. The program is cross-platform, and is available for a variety of operating systems, including Linux, Windows, Mac OS X, BeOS and others. Recently an offline web version of XaoS became available, being published at xaos.app. XaoS can show the Mandelbrot set (power 2, 3, 4, 5 and 6), the Octo fractal, three types of Barnsley's fractals, the Newton fractal (order 3 and 4), Phoenix fractal and Magnet (1 and 2). XaoS can display Julia sets from selected fractal parts. Xaos also allows users to enter custom formulas. Earlier versions of XaoS are capable of displaying fractals as ASCII art using AAlib, which, in combination with being built on freely available GNU tools, allows it to run almost anywhere. Newer versions use the cross-platform Qt library. An interactive help and an animated introduction to fractals are included. The introduction deals in ten chapters with different formulas presented in the software and their features.

Hubička algorithm XaoS was originally just a "poorly written" Mandelbrot viewer, until Jan Hubička added efficient zooming, using a technique sometimes called the XaoS algorithm or Hubička algorithm. At that time, fractal zoom movies were produced by completely recalculating each frame, even though they naturally had much of their area in common with each other. This made interactive zooming impossible without very powerful computers. Furthermore, unless even more processing is used in order to do antialiasing, recalculating every frame produces a 'twinkle' effect as small bright areas hit and then disappear between pixels. Yet allowing the user to zoom, rather than jump as in Fractint, seemed like the most natural way to interact with fractals. In order to create an interactive zoom, Hubička needed to find a way to save the calculations which were already made. It would take up too much memory to save every pixel ever calculated, so the Hubička algorithm only saves the previous frame, and rather than remembering the location of each pixel it can keep them aligned in rows and columns and remember those instead. The most difficult part of the XaoS algorithm was choosing which saved rows and columns to draw where. Doing this wrong results in distorted images, yet it must be done quickly to be useful. After several different heuristics were tried, eventually the problem was treated as an optimization problem. The remaining rows and columns are colored in the same as the closest row/column, and are freshly calculated as the CPU gets time to do so. This is a careful balance between keeping the zoom going and increasing the level of detail. Calculating areas where the image is being zoomed to is put at a higher priority since these will be on the screen the longest and this is likely where the user is looking anyway. Zooming out, the reverse occurs, and the priority is on the edges. The Hubička algorithm can also be applied to zooming in on other images where the pixels are calculated, and has been used in other software such as the rtzme ("Real-Time Zooming Math Engine") complex function graphing program, and other fractal zoomers.

References

External links

Official website XaoS on GitHub

Illustrations

Worked examples

Example 1 — a first encounter with XaoS

Start with the simplest possible case. Write down what XaoS claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to XaoS before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about XaoS ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of XaoS

In research: XaoS appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses XaoS in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: XaoS is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fractal software, Free mathematics software, GNU Project software, so understanding it makes those chapters shorter.
In everyday life: Look for XaoS outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study XaoS in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what XaoS means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain XaoS out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is XaoS in simple terms?

XaoS is an interactive fractal zoomer program. It allows the user to continuously zoom in or out of a fractal in real-time.

Why does XaoS matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study XaoS?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on XaoS.