Quilt of many colours

Hint:

Label the 26 columns with the letters A through Z.

Answer:

The quilt colours represent letter symmetries.

The red squares appear in columns

A, H, I, M, O, T, U, V, W, X, and Y, which exhibit vertical symmetry.

The blue squares appear in columns

B, C, D, E, H, I, K, O, and X, which exhibit horizontal symmetry.

The yellow squares appear in columns

O, Q, and X, which exhibit symmetry across the top-left to bottom-right diagonal (see the Q in QUILT).

The magenta squares appear in columns

H, I, N, O, S, X, and Z, which exhibit 180° rotational symmetry.

The cyan squares appear in columns

L, O, and X, which exhibit symmetry across the top-right to bottom-left diagonal (see the L in QUILT).

Finally, the green and white squares appear only in columns

O and X, which exhibit 90° and 270° rotational symmetries.

No squares are coloured in columns

F, G, J, P, and R, which exhibit no symmetries.

Regarding the colours themselves:

Red, green, and blue are the primary colours in the RGB colour model. The combination of horizontal and vertical reflections, represented by red and blue, is equivalent to a 180° rotation, represented by magenta, the combination of red and blue.

Similarly, yellow

is formed by combining primary colours red and green, and reflection across the top-left to bottom-right diagonal is equivalent to either a horizontal reflection followed by a 90° counterclockwise rotation, or a 90° clockwise rotation followed by a horizontal reflection.

Likewise, cyan

is formed by combining primary colours blue and green, and reflection across the top-right to bottom-left diagonal is equivalent to either a vertical reflection followed by a 90° counterclockwise rotation, or a 90° clockwise rotation followed by a vertical reflection.

Lastly, white

is formed by combining all three primary colours, and rotation by 270° is equivalent to the combination of rotations by 90° and 180°.