* The original color of the cactus: If the cactus is a dark green, the hair dye might not show up very well, especially if you're using a lighter color. If the cactus is a lighter shade of green or has some lighter areas, the hair dye will likely be more visible.
* The color of the hair dye: This is the most obvious factor. If you use blue hair dye, the cactus will likely turn bluish. However, the final color might be a mix of the dye color and the cactus's original color.
* The type and strength of the hair dye: Some hair dyes are more pigmented and vibrant than others. Also, some are permanent, semi-permanent, or temporary, which will affect how long the color lasts and how deeply it penetrates the cactus.
* The cactus type: Different cacti may absorb dye differently due to variations in their skin texture and composition.
Generally speaking, the cactus will likely end up being a slightly altered version of its original color, influenced by the color of the hair dye. The vibrancy and longevity of the color change are hard to predict without knowing the specifics of the cactus and the dye.
Important Note: Dyeing a cactus with hair dye is not recommended. The chemicals in the dye could be harmful to the plant.