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Title: In a line

pure

Please remember to state if your entry is pure, open or non-competing.

“There are two main goals for these contests: Fun and Glory.
Fun: You get only 4 days to create a cool image, based on the theme for the week.
Glory: After 2 days of voting, a winner is declared. The winner picks the theme for next week and will be featured in the Feature Row.”

(pure)
All work is done in blender, using python and blenders python api to generate the fractal and the tree + curve.

This is a visualisation of aspects of the famous Collatz-conjecture, of which Paul Erdös once said, that “Mathematics may not be ready for such problems”. It is about a very simple iteration:

start with a natural number

if it’s even, divide by 2

overwise multipy by 3 and add 1.

repeat.

The conjecture is, that this process always leads to the number 1.

Connection to the theme: it’s not just one series. You get a (mathmatical) series for every number!

What do I see in the image?

The iteration step can be represented as a function:
f(n) = n/2 if n is even, 3n+1 if m is odd

One can extend f to the range of real numbers using sine and cosine functions to alter smoothly between the conditions for odd and even numbers. Very brave ones even extend it to the complex numbers.

The fractal at the bottom shows, for with (complex) numbers the function f converges, if you extend f to the complex number plane. The visible range is ca 5 (left) to -7 (right) and ±1i. The big blob is around 0+0i. (If you’ve heard of the mandelbrotset before: there is a connection).

For the tree we can step back to the natural numbers and connect numbers if one is the iterative successor of the other:
64 → 32 → 16 → 8 → 4 → 2 → 1
3 → 10 → 5 → 16 → (see last line)
7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → (see last line).
As all these series (presumably) reach ‘1’ they must join the others at some point. Thus together they resample a tree.
The tree grows at number 1 of the fractal floor. Different angles to branch off were chosen, depending on various mathematical conditions.

The light curve represents the number line and goes through all the numbers (represented in my tree) in ascending order, thus snaking its way through the branches.

Blender 2.69, cycles render, pure. Very minor post work in paint.net. Remember WENN logo copyright to AMC (I think).

When I saw the subject my interpretation was favorite TV series. I see the entries have gone in other directions.

There was a short lived television series in the late 1990’s about a radio station in Pittsburg at the beginning of WWII. I really enjoyed watching it. It ran for 4 seasons and was renewed for more but an ownership change at the station cancelled it.

Pure. 3.3. Cycles.
As a kid I enjoyed John Gordon / Susan Cooper type stuff. This is based (very loosely) on The Dark is Rising book cover. Don’t think I read the whole series. Few bits to tidy up, if I get time…

I built this as a test for my Loop Nodes, so it’s a bit clunky and low-quality.

I decided to make the Fibonacci sequence, a well-known mathematical sequence that would be easy to implement with loop nodes.

x[n] = x[n-1] + x[n-2] # Python

The ship started as a suzanne and was entirely node-created. The exhaust from the engines is node particle systems (see further down in the loop topic). The nebula (the blue thing) was created with a strange update rule on loop nodes.

I haven’t figured out how to render the GN loops in the rendered view, so I rendered it in the viewport @ 4096 samples.

1.Open from blender,using a plane as the emittor from the top.
2.Using SVG format from illustrator,I managed to trace the title and just added the eye to the letter i.
3.I only used the eye as my imported asset.