Create a cylinder with lots of horizontal Loop Cuts using Ctrl+R and duplicate the cylinder 4 times. Give each cylinder their own material color and position as shown below. Select all cylinders and join them with Ctrl+J. Set the Origin at the center of the geometry and then apply a Simple Deform modifier with an angle 360° and select Axis the cylinder is pointing to, which is Z-axis in this case. Add Array Modifier to repeat the pattern.

Create a cylinder with lots of horizontal Loop Cuts using Ctrl+R and duplicate the cylinder 4 times. Give each cylinder their own material color and position as shown below. Select all cylinders and join them with Ctrl+J. Set the Origin at the center of the geometry and then apply a Simple Deform modifier with an angle 360° and select Axis the cylinder is pointing to, which is Z-axis in this case. Add Array Modifier to repeat the pattern.

Optionally you could give it this squarish look at the center by temporarily disabling the Simple Deform modifier and selecting the Edge Loops near the center for each cylinder then using Proportional Editing to scale the vertices toward the center.

Create a cylinder and duplicate it 4 times and position as shown below. Select all cylinders and join them with Ctrl+J. Set the Origin at the center of the geometry and then apply a Simple Deform modifier with an angle like 360° and select Axis the cylinder is pointing to, which is Z-axis in this case. You can also use angle 90° and then apply an Array Modifier to repeat the pattern.

Create a cylinder with lots of horizontal Loop Cuts using Ctrl+R and duplicate the cylinder 4 times. Give each cylinder their own material color and position as shown below. Select all cylinders and join them with Ctrl+J. Set the Origin at the center of the geometry and then apply a Simple Deform modifier with an angle 360° and select Axis the cylinder is pointing to, which is Z-axis in this case. Add Array Modifier to repeat the pattern.