Fibonacci Curve

[Rik]

Rik, here is my best shot.

Following the Fibonacci sequence (1, 1, 2, 3, 5 ,8, 13 21, 34, ...), I created a vertical line of unit length (here 50px).
I copied that and turned it 90° (horizontal) and created new lines the length matching the Fibonacci Sequence (above).

After running out of paper (A2), I switched to the Shape Tool and with Smooth Join, I touched each of the corners, moving along the line from in to out.

The trick is to choose a source point, just off the start point and to finish beyond the end point with a nearby sink point; these allow the sequence to be effectively truncated.

Fibonacci Curve.xar.

No guarantees it is right as the curves are Bezier but possibly more accurate than quarter circles.

Acorn

I can't say that I could follow all your instructions, but, the good thing was that you included your .xar file.

And when I place my curve made with semi-circles over yours, then there's a marked difference.
And if I download a Fibonacci Curve from the Internet and place my curve over the top, then it's pretty perfect.
And, I'm sorry to say that yours doesn't quite fit.

However, I am extremely grateful to you for trying to show me, and posting your file so that I could have a look at it.

[Acorn]

Rik, I must have got a bit dizzy.

Acorn

[gwpriester]

I created a continuous straight line tracing over Acorn's line segments, converted the control points to Curve, then clicked Make Curve (but first as suggested, added a tiny extra length at the start and one at the end) then it does indeed create a curve to match your results. And the beauty of vectors is once you have your right angles constructed, you can reduce the line to a more convenient size.

[gwpriester]

Since my vector line fibonacci spiral stereogram was so well received I decided to do another, this one using a blend of two curves.

[Acorn]

Since my vector line fibonacci spiral stereogram was so well received I decided to do another, this one using a blend of two curves.

Told you I got dizzy!

Acorn

[ernie-f]

My first thought:

[Rik]

My first thought:

Nice try, ernie.

But, that's not a Fibonacci Curve.
That's just a curve that's getting bigger exponentially.
I tried that.
And if you have a go, then try and put your exponential curve over the top of a Fibonacci Curve, then you'll see that they are not the same.

[gwpriester]

In all the time we have been going round and round you could have created the world's most exquisite Finonacci curve Rik.

[Egg Bramhill]

Problem with trying to use Xara's smooth bezier curves is they're not very good. Try creating a circle from four lines, converted to smooth curves. Definetly not a circle.

Inkscape has a better tool using it's spiro beziers.