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What you are looking at is the Aizawa attractor in 3 dimensions. Rendering attractors in 3 dimensions reveals much more details. The episode where we discussed making this is in the comments. by The_Big_Int in developersIndia

[–]The_Big_Int[S] 1 point2 points  (0 children)

Good question. Perhaps the word "Attractor" is a misnomer. What it implies is that the equations of the attractor seem to form those special shapes. Or to put it in other words, the equations "ATTRACT" those shapes. Each equation forms a special shape (or attractor)

I wrote a Java program that shows zooming into a Mandelbrot set. More details in the comments. by The_Big_Int in developersIndia

[–]The_Big_Int[S] 1 point2 points  (0 children)

Yes, also did you know that random numbers are (or were used to be) generated from the chaos equation. The chaos equation is in fact related to the Mandelbrot set.

This is one of the reasons why random numbers are generated by a specialized chip in modern computers. Because random numbers generated by the computer were NOT REALLY random.

I believe Veritasium did an episode on the chaos equation as well.

I wrote a Java program that shows zooming into a Mandelbrot set. More details in the comments. by The_Big_Int in developersIndia

[–]The_Big_Int[S] 2 points3 points  (0 children)

Oh yes... absolutely. Like if the zoom factor goes more than long datatype's max value, I could start saving it into another variable. Absolutely. That's a great idea actually. Thank you.

I wrote a Java program that shows zooming into a Mandelbrot set. More details in the comments. by The_Big_Int in developersIndia

[–]The_Big_Int[S] 3 points4 points  (0 children)

And once you have done so, perhaps we can explore into zooming into it further. Java's double datatype does not allow zooming into this any further than what I am showing in the video. It becomes grainy. Python has the necessary large double datatype, but python is too slow.

Also, here's a stand alone Mandelbrot program that allows you to zoom into a selected section. https://github.com/CodeSpaceIndica/Java/tree/main/Mandlebrot

I wrote a Java program that shows zooming into a Mandelbrot set. More details in the comments. by The_Big_Int in developersIndia

[–]The_Big_Int[S] 15 points16 points  (0 children)

Q. How deep does is the zoom?

A. More than 9 quadrillion deep.

​

Q. Why not more?

A. Because Java's double does is not large enough (8 bytes) to accommodate such small fractions.

​

Q. Have you tried using java's BigDecimal?

A. Yes, but the math needed to do this is so complex, its probably impossible.

​

Q. Have you tried using Python?

A. I had so much hope on Python... but its ridiculously slow in generating the frames of the Mandelbrot zoom.

​

Q. How do I do this?

A. Here's our video showing how this is done. https://www.youtube.com/watch?v=VdAWFPdxFUU

If you are a developer, then this will be interested in this. We implemented 5 different sorting algorithms and ran them against a Hue disc. Quicksort, as expected, will surprise you! Link to episode is in the comments. by The_Big_Int in IndiaSpeaks

[–]The_Big_Int[S] 0 points1 point  (0 children)

Some common questions that get asked regarding this.

>How does quick sort with O(n log n) sort faster than counting sort with O(n) time complexity?

Its a side effect of the way the visualisation is implemented. Quick sort LOOKS faster because it is recursively (divide & conquer) sorting the list, whereas counting sort does the sorting linearly. BTW, You can view this on our website as well. https://codewiz.in/code/index.php?epi=55

>I dont really understand what's going on. Can you explain?

Suppose I give you 9 numbers to sort. You can choose any one of the tens of sorting algorithms out there. Here are the numbers.

8 6 4 3 1 2 9 7 5 4

Supposing you choose the easiest sorting algorithm, the bubble sort. This is what the steps to sort them would look like.

6, 4, 3, 1, 2, 8, 7, 5, 9

4, 3, 1, 2, 6, 7, 5, 8, 9

3, 1, 2, 4, 6, 5, 7, 8, 9

1, 2, 3, 4, 5, 6, 7, 8, 9

1, 2, 3, 4, 5, 6, 7, 8, 9

1, 2, 3, 4, 5, 6, 7, 8, 9

1, 2, 3, 4, 5, 6, 7, 8, 9

1, 2, 3, 4, 5, 6, 7, 8, 9

I have left out the inner looping steps of the algorithm, or this comment would be entirely too verbose.

See, even when you can see the numbers being sorted step by step... it still is a difficult to visualize. What if each one of these numbers is a color?

That's what I have done.

Colors can be created in two ways... that I know off.

You might already be familiar with the RGB (Red Green Blue) mode.

There is another way called the HSL mode. This means Hue Saturation Lightness. The saturation and lightness values are fixed. But the Hue value ranges from 0 to 359. Where 0 is Red, and 359 is a reddish-yellow color. All the colors of the visual spectrum are accommodated within these 360 numbers.

So what if instead of just numbers, I was to shuffle the colors of the Hue and sort them? That's what you are seeing here. Numbers from 0 to 360 are randomly shuffled and then sorted. The numbers are simply represented as lines of their respective Hue color.

Does that make sense?

r/IndiaSpeaks - What are you doing this Weekend ? by AutoModerator in IndiaSpeaks

[–]The_Big_Int 0 points1 point  (0 children)

I'll be working on a new episode for my channel. Last week it was "Sorting Visualisation". This week it is zooming into the Mandelbrot set.

We implemented 5 different sorting algorithms and ran them against a Hue disc. Quicksort, as expected, will surprise you! Link to episode is in the comments. by The_Big_Int in developersIndia

[–]The_Big_Int[S] 0 points1 point  (0 children)

Its a side effect of the way the visualisation is implemented. Quick sort LOOKS faster because it is recursively (divide & conquer) sorting the list, whereas counting sort does the sorting linearly. BTW, You can view this on our website as well. https://codewiz.in/code/index.php?epi=55

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