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View attachment 2641180
my first Mac app, developed on Xcode 27, published via Xcode Cloud and ready to test 😊

… the best, it’s free


The corresponding iOS/iPad/AppleWatch version here


Saving favorites via the Cloud
 
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Nice, just out of curiousity, is it multi threaded and can use all cores? Does it use the GPU? Does it support higher precision than 64bit "double precision" floating point numbers?
 
Nice, just out of curiousity, is it multi threaded and can use all cores? Does it use the GPU? Does it support higher precision than 64bit "double precision" floating point numbers?

Thanks! 😊

  • GPU: Yes. Normal interactive exploration is fully GPU-accelerated using Metal, which keeps navigation smooth even at high iteration counts.
  • CPU: For very deep zooms the app automatically switches to a CPU-based high-precision renderer. At the moment this path prioritizes accuracy and stability over using all CPU cores aggressively, so there is still room for optimization.
  • Precision: The deep-zoom renderer goes beyond standard 64-bit double precision for coordinates, allowing reliable zoom levels of well over 10¹²× (and considerably deeper depending on the location).
The current high-precision implementation is just the beginning. I’m already experimenting with techniques such as multi-threaded CPU rendering, perturbation theory, and arbitrary-precision arithmetic, which should make much deeper zooms possible while also significantly improving rendering speed.

My goal is to keep the app easy to use while continuously pushing the practical zoom limit further.
 
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Thanks! 😊

  • GPU: Yes. Normal interactive exploration is fully GPU-accelerated using Metal, which keeps navigation smooth even at high iteration counts.
  • CPU: For very deep zooms the app automatically switches to a CPU-based high-precision renderer. At the moment this path prioritizes accuracy and stability over using all CPU cores aggressively, so there is still room for optimization.
  • Precision: The deep-zoom renderer goes beyond standard 64-bit double precision for coordinates, allowing reliable zoom levels of well over 10¹²× (and considerably deeper depending on the location).
The current high-precision implementation is just the beginning. I’m already experimenting with techniques such as multi-threaded CPU rendering, perturbation theory, and arbitrary-precision arithmetic, which should make much deeper zooms possible while also significantly improving rendering speed.

My goal is to keep the app easy to use while continuously pushing the practical zoom limit further.

this is currently a zoom of nearly 8e+12 with initial Perturbation, but still playing on radius and arbirtary precision ...
Screenshot 2026-06-29 at 14.09.29.png

... just at the edge of current precision.

[ btw. if you consider the initial magnification being the size of our Milky Way, at roughly 7 trillion times magnification, the scale is comparable to zooming from the entire Milky Way down to an area only about 135,000 kilometres across — well within the Earth–Moon distance. ]
 
Perturbation:
Screenshot 2026-07-04 at 07.27.10.png


new build 2.3 allows to use experimental rendering like perturbation and double-double-cpu (which will take over at defined zoom levels (Perturbation >2B). They increased details in deeper zoom levels but at severe impact on calculation times - you can always break by Undo or any new selection).

Double-Double:
Screenshot 2026-07-04 at 07.30.29.png


and - to compare - default High Precision - CPU Deep Zoom:


Screenshot 2026-07-04 at 07.32.47.png

and the High Iteration Deep Quality, which can change the appearance significantly.
Screenshot 2026-07-04 at 07.38.07.png
Screenshot 2026-07-04 at 07.40.59.png


 
Last edited:
BeautyOfFractals-EightRainbows-Rainbows-1750-iterations-2880x1800.png


new version 2.4 introducing Celtic and Eight Rainbow mode (a Mandelbrot based on z > z^8 + c) with new areas to discover
 
Oh wow, just saw this post, going to check out the app now. First started viewing fractals using FRACTINT! On my 386SX in the early 90s (you can imagine how slow calls were without the dedicated floating point unit of intel’s DX chips).
 
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Oh wow, just saw this post, going to check out the app now. First started viewing fractals using FRACTINT! On my 386SX in the early 90s (you can imagine how slow calls were without the dedicated floating point unit of intel’s DX chips).

Thank you! FRACINT on a 386SX is a wonderful reference point — quite a contrast to exploring deep zooms interactively today. I hope you enjoy the app, and I’d be very curious to hear what you discover.

I have had more or less the same - painful - history, That's why I started the project as reminiscence to old times 😉
 
Just submitted a new version to Appstore/Connect which dramatically improves deep zooms ... 3.4e+15 on the iPhone in less than 20 sec

BeautyOfFractals_macOS_2_5_Deep_Precision_2880x1800.jpg
BeautyOfFractals_iOS_2_4_Deep_Precision_1290x2796.jpg
 
Cool. Can you export a movie between 2 coordinates?
Not yet — currently it exports high-resolution PNG stills.

But that is a great idea. A guided movie export between two saved coordinates / favorite spots would fit the app very well, especially now that deep zoom rendering is much more stable. I’ll keep it on the roadmap.
 
invented Triple-Double ...

1783964056448.png

New limit at e40 ... (but ... in crazy speed)

And - btw. - modernized the menue bar a bit and you can hide/unhide it with Shift-Cmd-C now ...

(v.2.10 - currently in review)
 
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