“The color of shell is a factor of diet. You can change the color by changing the diet.”
The color of chicken eggs is genetically determined. You may get slight changes by changing the diet. A white egg may be off-white but will never be brown; and brown, blue and green eggs will always be shades of those colors.
What really is affected by diet is the color of the yolk.
From chickens with a grain only diet, the yolks are yellow.
Add some grass or other greens to the diet and the yolks become orange-yellow.
Add some insects and worms to the greens and the yolks will be a bright orange, regardless of the shell color.