aspects of camouflaged
Mantids are some of the top predators of the insect kingdom, however that doesn't mean they're not eaten as well. Because they are both hunters and prey, their behavior and anatomy evolved to maintain this balance.
Nearly every mantis species has some sort of mimicry in their anatomy. They will have extensions to their exoskeletons that resemble leaves, branches, moss or even flowers. Their colors are often tuned into their environment, blending in seamlessly with their surroundings. Their behavior only heightens this camouflaged.
Movement
For the most part mantids will sit motionless in a spot that best resembles their camouflaged to wait for prey. They are ambush predators, waiting for their prey to come to them. Most species will hang upside down as a way to maximize the usage of those front raptor claws. To any predator near by they just look like an ordinary stick or leaf. As pets they still maintain this behavior and will often hang from the top of their habitat.
When they do move, they will often walk with a slow choppy gait, to mimic the movements of foliage blowing in the wind. They can run, and very fast at that, using all all six limbs to climb and hop on nearly any surface.
Threat Displays
When running and hiding don't work, mantids will show a threat display. They spread their legs in a stance with their thorax facing the threat. The abdomen and wings spread out showing as much surface as possible. This display is an attempt to appear larger than they actually are, deceiving the predator that they might be too big to eat.
Most species will have patches of bright colors on the underside of their arms and the second pair of wings. The threat display flashes these colors as a warning.
Usually bright colors mean toxicity. Though not toxic, they might just fool a predator into thinking they are not very palatable. Some will have spots that mimic eyes.
Color Morphs
Almost every species has some variation of color differences between individuals. Even siblings can have different colors. Colors can also change between molts. There are several factors that play into this.
Most species will be colored depending on their environment. They will try to match their surroundings. But sometimes colors are dependent on humidity levels. Ghost mantis have a large range of colors from olive green, light browns to even black. The more humidity, the more green they will be.
There is also a genetic factor to it as well. Some populations will differ in color from others and can be interchanged via breeding. If you want your mantis to be a particular morph, you have to take all these factors into consideration. Adding more flowers or bright colors might bring out more pinks or greens to some species. More branches could bring out more browns. Traits from one individual can sometimes be passed down into the next generation.