A perfect representation of the Golden Ratio originally designed in Inkscape and remade in Gravit Designer!

You can view/edit the code on Codepen: https://codepen.io/michaelsboost/pen/Mr ... itors=1000

The template also comes with the Golden Ratio Spiral as well. (It's just a hidden group)



SVG file is also available for download:

It cannot be "perfect" if you have the two equal smaller circles (which are each one half of the immediately bigger circle, while one should be 0.618 times that).

Btw, your graphic a good visual proof that

I think having two equal smaller circles is correct.

See here:
https://www.mathsisfun.com/numbers/fibo ... uence.html
0, 1, 1, 2, 3, 5, 8, 13, 21, 34

There should be no end... Each time you have a rectangle (which is 1:1.618..), you cut a square out of it, and you are left with a smaller rectangle which is itself 1:1.618, in which you cut a square, etc... and you repeat ad nauseam (of course, with bitmaps you stop when the rectangle is about one pixel...) (because one property of the Golden Ratio is that 1/ϕ=ϕ+1).

I think it works the other way round. Start with a small square and keep increasing (which is what the OP has done). But early in the sequence you get 2 squares of equal size.

The ratio of 1.618 only appears after several iterations.

I'm out of my depth with the maths but the way I understand it from my art college teaching is that the page is divided so that the smaller part is to the larger what the larger is to the whole. This division of a page suggests to me that Ofnuts is correct and you in fact subtract.

I looked up Golden Ratio on wikipedia, and it seems ofnuts is correct. Because what the OP has is the Fibonacci Spiral which approximates the golden spiral (which starts with 2 equal squares and not a golden ratio every step along the way) (not exact, therefore not "perfect").

Here's a more "perfect" golden ratio grid (of course only accurate to 3 decimal places as Inkscape allows).


zipped .svg (with guides accurate to 3 decimal places).

I'm pretty sure you know enough Python to script that down to sub-pixel squares. You only need log(1000)/log(ϕ)≈15 iterations.

Good on mikethedj for this code and graphic. Seems that the 'golden ratio' or phi is an irrational number so the discussion cannot be decided mathematically. Agree with ofnuts that it doesn't look right. It would have to be a recursive representation of circles going on to infinity.
Could be a Droste effect like this:

but i wanted to try out inkscape.

That can be scripted in Python too

Curiosity got the better of me so I decided to check out the difference between Fibonnaci and Golden Ratio. Ofnuts was correct.

I constructed a Fibonnaci spiral and a Golden Ratio spiral. (I used Inkscape Spiro Path to draw the curves - this is slightly off but the same error for both spirals.) I then superimposed the 2 spirals.

On a low res bitmap image like I created there is no perceptible difference. Mathematically the 2 are different but as a layout tool for an artist they can be considered the same.