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### Author Topic: (Other) Baroque Symmetry  (Read 285 times)

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#### ThunderboltPagoda

• Fractal Furball
• Posts: 254
##### (Other)Baroque Symmetry
« on: July 16, 2020, 02:45:59 PM »

Music:
Johann Sebastian Bach: Brandenburg Concerto No. 3 (BWV 1048), 1st movement
This recording: Advent Chamber Orchestra
https://freemusicarchive.org/music/Advent_Chamber_Orchestra
Released under Creative Commons license CC BY-SA 3.0 US
https://creativecommons.org/licenses/by-sa/3.0/us/

Visuals:
A succession of Lyapunov fractals, as usual created with Lyapunov Pagoda.
Iteration function: f(x) = b×sin(x+r)×sin(x-r)
Sequence: bac

In my first videos, I used the parameter b in the iteration function to create motion, and in my latest videos, I used the c in the sequence of 3-D Lyapunov fractals for that purpose. Here is my first video that combines both methods.

a and b in the sequence are the x- and y-axis in the images, c is the z-axis which is translated to time in the video. The formula creates reflectional and translational symmetry in all spatial dimensions (which would be better visible on a larger scale). If the increment of c is constant from frame to frame (which is the case here), the spatial symmetry in the z-direction would be translated to a temporal symmetry in the video. But the temporal symmetry is broken, because b in the iteration function (not to be confused with the b in the sequence) is also increased (from 1.8 to 2.6) throughout the video. c runs from 0 to about 23.56, which is pi × 7.5. So the video consists of 7 and a half cycles, but nothing ever repeats.

A high resolution (1600*1200) version of the video can be downloaded here (JavaScript and cookies required).

This video is released under Creative Commons license CC BY-SA 3.0 US.

Linkback: https://fractalforums.org/index.php?topic=3663.0

#### gerson

• Fractal Frankfurter
• Posts: 572
##### Re: Baroque Symmetry
« Reply #1 on: July 27, 2020, 11:15:21 PM »
this formula gives nice simetrical images and now videos...

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