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Currently I am using XaoS to view fractals. However, when zoomed in too much, it gets pixelized and I can't zoom in any more.

enter image description here

How can I use this program, or some other program, in a way which allows me to zoom in forever in a fractal?

Rookie
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    Respectfully, you asked this yesterday and it got closed. You already know that XaoS won't do the job. Instead of asking us to give you a list of programs, use google. – Everett Aug 14 '12 at 13:33
  • Could you provide a screenshot of this? And maybe explain how you're using the application. Because XaoS does not produce any pixelated output for me. – Oliver Salzburg Aug 14 '12 at 17:16
  • @OliverSalzburg, here: http://minus.com/lEAzFITfW6VZV - simply zoom in as long until that happens... – Rookie Aug 14 '12 at 21:23
  • @Rookie: I had installed it for the first time ever a few hours ago. I left all settings at default and just started zooming in. So far until there was no more detail in that area. That took about a minute. I did not see that pixelation happen at all. It was perfect fractal zooming, just like I would have expected. – Oliver Salzburg Aug 14 '12 at 21:37
  • @OliverSalzburg: maybe different compilation options? The one in the Ubuntu repos exhibits the bug. – Mechanical snail Aug 14 '12 at 22:40
  • @Mechanicalsnail: Interesting. I used the Windows version. – Oliver Salzburg Aug 14 '12 at 22:41
  • @OliverSalzburg, use enough iterations (20000) and set the zoom speed to 5, so you can reach the end faster than in a minute. – Rookie Aug 15 '12 at 11:15
  • @Rookie: Okay, now I can reproduce it as well ;) – Oliver Salzburg Aug 15 '12 at 11:31

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This is probably better suited to Math, but in this form, the question actually does apply to computers as well in a way.

Computers represent numbers with bits. Fractals are created with real numbers (numbers with fractions/decimal places). Unlike integers which are nice and straight forward, real numbers are a little trickier to implement in computers. Regardless, just like integers have limits on the range of number that can be represented (n number of bits allows for 0-2n positive numbers), floating point numbers also have limits to the numbers that can be represented.

Because of the limits, there is only so much detail that a fractal viewer can show. At some point, the program can no longer calculate precise enough numbers. As a simplification, lets say that the maximum precision that the program can represent is 10 decimal places. After that, numbers just get rounded to the nearest 10 decimal places, regardless of the calculation.

Fractals start out fairly simple, but quickly explode to real numbers with many decimal places after just a few levels of zoom. That is why when you zoom in for a bit, the program can no longer provide the precision (number of decimal places) required to provide accurate, detailed edges to the fractal and ends up just rounding it out both mathematically, which depending on the program may result in pixelation or rounded, non-detailed/fractal edges (some programs just take it a step further and limit the amount you can zoom in the first place).

The limitations depend on both the hardware and software. You can improve the quality by using a system with 64-bit hardware, lots of memory, and software that can take advantage of them.

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Synetech
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  • Since fractals are self similar, a zoom need only be a zoom by name. It does not actually have to zoom at all. – soandos Aug 14 '12 at 17:47
  • True, but how would you write a program that can detect when it is similar to a higher level? You would still need a way to calculate the edge. This becomes difficult because the user is free to choose where to zoom, so you would need a table of values or something. – Synetech Aug 14 '12 at 18:50
  • I know the limitations of computers, but if we increase the bits the deeper we go, then we can say its infinite zoom; only the memory is our limits. I know there are such programs, i saw youtube video about some guy making fractal that zoomed in so long it took 2 months to render. and there are programs that allow N bits numbers (practically any size number possible to operate calculations on), so why not fractals with N bits? – Rookie Aug 14 '12 at 21:15
  • i dont think the quality will get better with 64bit system; as far as i know, even 32 bit systems support double precision (64bit float). its only a matter of increasing the size of the float values, and you dont need a N bit computer for doing it, 32bit computer can do any size numbers, but ofc it will be slower to process than with 32+N bit computer. – Rookie Aug 14 '12 at 21:18
  • @Rookie, the precision is the main limit. The program the guy you are thinking of was specially written (like programs that calculate PI to a massive number of decimal places). Using a 64-bit system simply makes it easier because less work has to be done in software and more of the calculations can be done on-die. – Synetech Aug 14 '12 at 21:44
  • @Rookie Fractals with N bits do exist. I'm making a program now based on the new perturbation theory maths to take the rendering time of that 2 month video to 2 hours. For programs that have N bit rendering, see Fractal Extreme, Ultra Fractal 6, or Kalles Fraktaler (this is free and it's the fastest) – Byte11 Nov 29 '17 at 01:55