illustration - Designing a logarithmic/phyllotactic-like pattern in Illustrator

After watching today's Apple Keynote, I witnessed a modal used in one of the HomePod slides. It shows a mesh design for the fabric that encloses the device.

How might I reproduce this in Illustrator? At least the shape. Not the entire gradient color and shading.

I'm assuming I'll need to create a spiral graph, however I am having a hard time doing that in Illustrator.

Answer

Here goes for the shape...I can further my answer tomorrow if you require more help for shading.

1. Create an elliptical shape in Illustrator.



2. Rotate it by 137.5 degrees and copy it. (Also known as the Golden Angle...this is key!)


3. Hit ctrl+d or cmd+d to duplicate until your shapes start to seem thicker (that means you went too far so you can undo until you have a nice, uniform texture).


4. Cover the center with a circle. Go on with recreating the shading!