Here is an image by David Rudnick. I would like to create the checkered effect, been trying with illustrator but no luck. It seems like this was either wrapped on an existing object, or 3D extrusion.

If someone could lend a hand that would be fantastic! :)

I used Plain-jane Illustrator, no plug-ins, and created simple rectangles, scaled and placed with smart guides on for snapping, placed an alternating row of them, then made both the alternating rows a symbol.

I used the direct selection (white arrow) tool to select all the outer edge anchor nodes, and pulled them back the correct amount to get this effect.

No tricks, no filters. Simple.

I only took it a small distance - you can keep going till the chevrons are very small, and you'll get materially the same effect as the example image.

Actually the major idea is already shown by user GeradFalla - except the right spacing. The original stripe obviously wants to be like a 3D revolution surface, so let it be. Unfortunately 3D in Illustrator is a little poor, so we solve and draw the projection in 2D.

1. Draw a 40-gon with the polygon tool. By holding shift force a side to be the uppermost part. Be sure you have no fill, only a stroke. Then rotate the shape 4,5 degrees to make one corner to be the uppermost point.




2. Delete 3/4 of the 40-gon. Leave a 90 degree polyline sector between9 and 12 o'clock. I have splitted and colored the segments only to show them. For the work splitting and coloring is useless.




3. Have Smart guides and snap to point ON, no other snaps. With two vertical lines (black) and horizontal lines from the nodes of the polyline draw the borders of a well spaced stripe

4. Select the line grid. With the shape builder fill the rectangles with 2 solid colors. Do not use black nor white here.




5. Remove remnants and strokes. You should now have this stripe of rectangles. Group it.




6. Double click the shear tool and set vertical shearing 30 degrees. Apply it to the stripe.

7.Goto Object > Transform > Reflect > Vertical and make a flipped copy of the stripe. Then goto Edit > Edit Colors > Recolor artwork and recolor the stripes to opposite Black and White. I used light grey instead of white to make the stripe fully visible.

Now you have the needed stripes ready to clone and tile.

Envelope Distort....

Checkered pattern-filled rectangle, Object > Envelope > Make with Mesh.

Then move, add/subtract, mesh points with the Mesh Tool and distort till your heart's content.

_{This isn't quite the same checkered pattern, but it's close enough to show the theory. Realize this is a very quick demonstration of the features its not a direct attempt to mimic the sample image. More care would be needed to create the proper checker pattern and adjust the mesh points. It can be done using this method though and there would be no need to draw every piece of the pattern manually.}