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Japanese wheel pattern

Adobe Illustrator- Japanese Wheel Pattern
This is a pattern I have seen a few times in Japan. It evokes the idea of a wagon or cart wheel.
Getting the base shape is fairly easy. First, create a circle. Mine is 250px by 250 px.

Second, create a copy of that circle and move it down so that it overlaps the edge of the original. My copy is moved 175 px vertically and I have changed the colour of the copy to orange with a black stroke so it is easier to distinguish.

Third, using the rotation tool, hold the alt key / option key and rotate the copy around the center of the original circle by 120 degrees to make another copy in a new position. Then, use control+d / command+d to create a third copy.

Finally, you can use the pathfinder options or shape maker tool to subtract these copies from the original circle and we have the base shape. With the base shape, you can add a stroke that's aligned to the center.
Now with the base shape, you can use either the Object->repeat or Object->pattern options. First, use the grid option and brick-by-column. Then, move the individual objects closer so that the edges touch. For my image that was -96 px horizontal and -44px vertically.

A wide variety or results can be created using minor alterations to this method.
Japanese wheel pattern
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Japanese wheel pattern

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