Vacations 01 - Rhodonea!

in #fractal5 years ago (edited)

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You might be familiar with the rhodonea curves, from your childhood: there was a simple toy where you fixed a gear into a frame, and put a pencil in one of the many holes of the gear; then, as you rotated the gear inside its frame, it made a sinusoid movement, with the pencil tip drawing curves like these:
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By Jason Davies, CC BY-SA 3.0, Link

My fractal started as a simple combination of rhodonea and circlize variations. The second variation is three times more prominent in this case, and distorts the rhodonea curves in a circular fashion around itself. I used a subtle coloring for the background and some extra noise in the rendering, in order to give a feeling like we are seeing a parchment with scribbles in black ink.
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The result was too symmetric for my taste; I tried to break the symmetry by the power of my favorite moebius variation. While the moebius strip & its properties are too hard theoretical stuff to explain here*, let's just say that it produces excellent designs in the fractal realm. And... it breaks symmetries!

* check this excerpt from wikipedia: "[It] is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary. The Möbius strip has the mathematical property of being unorientable." Want to know more? Really?!? Then, go here.

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Of course, in every step things had to be moved around, tweaked in the second & third decimal places, rotated and scaled, until the shapes blended into a proper design and made some kind of sense. So, I had to cover the white space in the edges and I tried many different effects until I ended up with something I liked: boarders!
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Split boarders to be more precise, the variation that produces the square cells in the image above. I liked the transitions from the rhodonea curses to the angular boarders so I kept them. I had to make a lot of arrangements and experimentation with the relative weights of each variation until I got the final result, the original Vacations! - the origin of Vacations 02 I don't know why that word came up to my mind when I saw the final design, but it did...

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Vacations

by @nyarlathotep
A fractal made in JWildFire

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This is really cool! I found you thanks to @katharsisdrill! These are like using the old spirograph! I had old toys from before my own generation thanks to having really old older siblings and I remember the old carboard box, like a boardgame box, full of these little plastic discs and wheels and putting in a pen or pencil and making wonderful seemingly random patterns.

Heh, I have the same memories of spending so much time trying different patterns! Now, try to realize that all those "seemingly random" shapes are in fact perfectly described by mathematical formulas; changing the numerator and denominator of the formula gives the different shapes (in the first picture above, the numbers on the sides are numerator and denominator, n/d).

It is baffling. I have a dear friend who is a bit of a Math genius and he can go on and on about fractals, though I don't always get it, I do see the beauty in Maths, even poetry, in some way, is Maths, I believe.

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