Recamán's Sequence Curve (Curly As)

[Boleeman]

Recamán's Sequence Curve

A sequence defined by a recurrence relation.

Read about it here:
https://en.wikipedia.org/wiki/Recam%C3%A1n%27s_sequence


Enjoy.

[TRon]

Nice Boleeman.

It so happens to be that I was literally just reading up on Recamán's curve (well actually watching a vod) because I thought you was not running into that equation in the foreseeable future (obviously I guessed wrong there) . You can do nice things with it, including using it for generating sounds.

[Boleeman]

Hi there TRon.

What interested me about Recamán's Sequence Curve was the way it goes into a loop, then gets out of it into another looping episode, and  this cycle continues. Every so often it does just a few loops. Sort of reminds me of electronic orbitals in atoms that I learnt about in my university days. The Recamán loops sort of out of the ordinary and quite different to Fermat's Spiral (just did a version of that too recently = this morning before work).

Thaddy was also talking about the De Jong Attractor to be able to be used in music and you said that the Recamán curve can also be used in music. Would maybe want to investigate that further (one day).

wikipedia also stated:  "Besides its mathematical and aesthetic properties, Recamán's sequence can be used to secure 2D images by steganography"


Regards Boleeman (Ed.)

[TRon]

Hi Boleeman,

What interested me about Recamán's Sequence Curve was the way it goes into a loop, then gets out of it into another looping episode, and  this cycle continues. Every so often it does just a few loops. Sort of reminds me of electronic orbitals in atoms that I learnt about in my university days. The Recamán loops sort of out of the ordinary and quite different to Fermat's Spiral (just did a version of that too recently = this morning before work).

The vod I was watching described it as ordered chaos and I tend to agree with that. Not being a mathematician these kind of things amazes me, just like fractals do. In comparison it is fairly simple math that is able to create patterns that you would not believe for them to be possible. Recamán theory really shows that with such simple rules and some of the the variations behave even more strange. A person might become completely lost in such things (for sure I do).

Thaddy was also talking about the De Jong Attractor to be able to be used in music and you said that the Recamán curve can also be used in music. Would maybe want to investigate that further (one day).

Too much to learn, so less time to do it in/with :-/ I is on my agenda as well.

wikipedia also stated:  "Besides its mathematical and aesthetic properties, Recamán's sequence can be used to secure 2D images by steganography"

Indeed the pattern can be used to hide messages in f.e. bitmaps. The vod I watched briefly touched the subject (similar to how the sequence can be used to create sound-patterns).

Anyhows, in case beating me to it and in case wanting to know more about converting to sound-pattern or audio in general then feel free to give a shout, I should be able to help with that.

regards,

PS: one of the reasons I came across Recamán was because I was reading up on a completely other (unrelated) topic which somehow got me side-tracked to something named the coding-train which mentioned Recamán. They might perhaps be of interest to you because it seems they cover applied math for creating or solve graphical related topics. Seems mostly typscript but that is easy enough to follow.