## A Fractal in Time

### Re: A Fractal in Time

Those are awesome! Spiral!!! Wow, there's a lot of potential with that.

*amor fati*

### Re: A Fractal in Time

You created a version of a chambered nautilus. Very interesting information here:

https://www.math.duke.edu/education/ccp ... equi1.html

Even more awesome, your first pattern is similar to this.

Yours is a bit different I think. I wonder if a closer approximation is possible: I'm guessing the ratios would be difficult to get right.

If it's possible, it would be a version of the golden spiral

http://mathworld.wolfram.com/GoldenSpiral.html

https://www.math.duke.edu/education/ccp ... equi1.html

Even more awesome, your first pattern is similar to this.

Yours is a bit different I think. I wonder if a closer approximation is possible: I'm guessing the ratios would be difficult to get right.

If it's possible, it would be a version of the golden spiral

http://mathworld.wolfram.com/GoldenSpiral.html

*amor fati*

### Re: A Fractal in Time

A different possibility might be the Fibonacci spiral. The numbers could potentially work out: e.g., some multiple of 8 iterations, 5 iterations, 3, 2, 1, 1.

*amor fati*

### Re: A Fractal in Time

Yeah it's exactly that spiral in the link you've posted Not the Golden Spiral though. Should be doable too though. Now I want that

**Perfection hasnt reached me yet, but its trying hard!**

### Re: A Fractal in Time

Alast - Can you post or PM your triangle tessellations? I can almost get the nautilus but not quite. I'm not sure how you did the other.

*amor fati*

### Re: A Fractal in Time

Sure thing Here they are. The only difference between those 2 is actually the split angle of the initial cell

https://www.dropbox.com/s/t5y0ejmpdqcj9 ... enome?dl=0

https://www.dropbox.com/s/1gvrtaqf7fd77 ... enome?dl=0

I think for a Golden Spiral we'd need a new genome though. Trying to connect a cathetus of a smaller triangle with the hypothenuse of a larger one builds up tension between the 2 triangles from iteration to iteration corrupting the desired shape.

https://www.dropbox.com/s/t5y0ejmpdqcj9 ... enome?dl=0

https://www.dropbox.com/s/1gvrtaqf7fd77 ... enome?dl=0

I think for a Golden Spiral we'd need a new genome though. Trying to connect a cathetus of a smaller triangle with the hypothenuse of a larger one builds up tension between the 2 triangles from iteration to iteration corrupting the desired shape.

**Perfection hasnt reached me yet, but its trying hard!**

### Re: A Fractal in Time

Hey, if you just start your Sierpinski with your mode 16, you get the same result with less modes used

**Perfection hasnt reached me yet, but its trying hard!**

### Re: A Fractal in Time

Sweet! I figured there was probably a way to reduce modes. But in trying to work it out the pattern, I maximized modes to maximize my ability to manipulate cells independently of one another.

The Fibonacci spiral would definitely require something different than this genome. Its triangles are each double the size of the next smallest one -- 2, 4, 8. Fibonacci has 2, 3, 5...

That said, your triangle almost has its 2, 2, 4, 8, 16 in exactly corresponding positions. There would be two changes. The green, green, red, blue arc would be all green. The yellow arc next to it would be black. And that completes the same pattern using squares of 2 rather than Fibbonacci numbers.

The Fibonacci spiral would definitely require something different than this genome. Its triangles are each double the size of the next smallest one -- 2, 4, 8. Fibonacci has 2, 3, 5...

That said, your triangle almost has its 2, 2, 4, 8, 16 in exactly corresponding positions. There would be two changes. The green, green, red, blue arc would be all green. The yellow arc next to it would be black. And that completes the same pattern using squares of 2 rather than Fibbonacci numbers.

*amor fati*

### Re: A Fractal in Time

PS. That would create a spiral where each seqment would be a quarter-circle with a diameter double of of the next smallest one.

*amor fati*

### Re: A Fractal in Time

The iterations of the Sierpinski carpet have an interesting alternation of patterns. Pretty cool!

*amor fati*