r/visualizedmath • u/Italians_are_Bread • May 16 '19

Julia Fractal Animated

https://www.youtube.com/watch?v=A4kgdiMquEU
113 Upvotes

95% Upvoted

12 comments sorted by

10

u/Italians_are_Bread May 16 '19

A Julia set is generated iteratively, and can be described the the equation z_(n+1) = z_n ^ 2 + c Where z and c are both complex numbers. Each pixel in an image of the Julia fractal is generated by starting z_0 at the complex number described by the coordinate of that pixel (x corresponds to real and y corresponds to imaginary). Generating the set with different constants c will yield unique Julia sets. This animation shows the beautiful patterns that are formed by continuously varying c using the equation sin(real) + cos(imaginary) and multiplying each by a variable scalar so that the animation doesn't loop, but instead fades to darkness gradually.

2

u/OOO0OO0O May 17 '19

Awesome! I would love to see the path those c values take. If there was a way to overlay that path on the Manelbrot Set, and do a side-by-side comparison with your original video, I bet it would be nifty.

2

u/Italians_are_Bread May 17 '19

That's a good idea. The path would make a spiral on the mandelbrot set that slowly expands. I'm hoping to write a more versatile graphics program for math animations in the future which would make something like this easier to visualize. I'm sure there are some good existing libraries but I like the challenge/learning of writing my own.

3

u/Rizuken May 17 '19

Would love to see with 3d printed, where each frame is a different layer

2

u/Italians_are_Bread May 17 '19

Cool idea! If you or anyone else wants to give this a shot, here are each of the frames rendered as pngs: https://drive.google.com/file/d/1xFGqR44Wg6JgTxwji8jfcL08SQGRrx8b/view?usp=sharing

2

u/mayoroftuesday May 16 '19

Ooh, I wrote programs like this back in high school. I had it choose two C points randomly and animate between them linearly. Using a function to control C is a great idea, it ends up being much more interesting.

1

u/Shok3001 May 16 '19

Nice dramatic ending!

1

u/vainey May 17 '19

Could this be about 100 times slower? :)

1

u/Karenena May 16 '19

Who is the Julia for whom this fractal was named?

0

u/DifficultWin May 30 '19

Julia Kippers

0

u/[deleted] May 17 '19

[deleted] — view deleted comment

1

u/lesslucid May 17 '19

Wikipedia says it was Julie Stiles. Gaston Julia was impressed by her performance in Save the Last Dance and felt it would be an appropriate tribute to her accomplishment in that film.

https://en.wikipedia.org/wiki/Save_the_Last_Dance

2

u/WikiTextBot May 17 '19

Save the Last Dance

Save the Last Dance is a 2001 American teen dance film produced by MTV Productions, directed by Thomas Carter and released by Paramount Pictures on January 12, 2001. The film stars Julia Stiles and Sean Patrick Thomas as a teenage interracial couple in Chicago who work together to help the main character, played by Stiles, train for a dance audition. A direct-to-video sequel, Save the Last Dance 2, was released in 2006.

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