Organic but perfect geometry

Studiobaum,

After pulling my socks up, here is the careful construction with fuller than normal Bezier circle accuracy, where the identical repeated shapes only consist of circular arcs, just drawing and letting Illy (job description Adobe Illustrator) make the necessary fitting by snapping in place without calculations, starting with the use of a free script.

This is (also) very simple to adapt it to any other number of shapes than 7, just by replacing 7 by that number as the basis for the free script and then doing everything in the same way.

You can see the steps below with the arcs taken from the original circles and the bounding circle and with a colour wheel adapted for 7 colours; you can Click the image to enlarge and see details.

If you wish, I can specify the steps.

Click to get closer, Click again to get closer still

Studiobaum,

I finally found the time for a careful construction with full (normal Bezier circle) accuracy, where the identical repeated shapes only consist of circular arcs, just drawing and letting Illy (job description Adobe Illustrator) make the necessary calculations and the fitting by snapping in place.

It is very simple to adapt it to any other number of shapes than 7, just by replacing 7 by that number as the basis for the initial calculation made by Illy and then doing everything in the same way.

You can see the steps below with the arcs taken from the original circles and the bounding circle and with a colour wheel adapted for 7 colours; you can Click the image to enlarge and see details.

If you wish, I can specify the steps.

Click to get closer, Click again to get closer still

Let me add another one. This uses an additional fill in the Appearance panel as a helper object to position the circles. You need to zoom in a lot to eyeball the most accurate position. Live Paint and Pathfinder finish the job,

You need some helper objects and you need to be very careful with smart guides. Take care that you are scaling proportionally (smart guides show that with a remark). In the preferences for smart guides you need to turn on all the options.

https://youtu.be/1uZ8PaJY5Wo

Studiobaum,

You can try the following:

1) Create two circles touching each other with coinciding side Anchor Points, abutted horizontally;

2) Delete the upper left quarter of the rightmost circle (1 segment deleted), and delete all but the upper right segment of the leftmost circle (3 segments deleted);

This will give much of the shape;

3) Join the two circle parts, at the coinciding side Anchor Point and between the top Anchor Points;

Now you have a straight version of the basic shape:

4) Move 7 copies horizontally by the (original) diameter so you have 8 abutted shapes in total, then change the colours as desired, starting and ending with the topmost one in your image;

5) Cut the two outermost shapes at the top and bottom Anchor Points and delete the outlying parts so you have two partial shapes at the ends;

6) Turn this set of shapes into an Art Brush, remember to tick Proportional;

7) Create a circle corresponding to the centres of the original circles, remember to cut it at the topmost Anchor Point;
😎 Apply the Art Brush to the circle from 6).

There is an inherent distortion, but that is inevitable to get things to fit, so this may by the least worst.

Edit: Sorry, I was in too much of a hurry because of other things.

I just found the time to try it out, and it fails to work properly. It has to be done with careful construction.

This goes to prove the old saying: play it before you say it; or just remember what you actually know.