Entropy: Chaos or is it really Order?

I do not understand why my old Biology book explains Entropy as the universe moving towards chaos. Spontaneous reactions take no energy; therefore they move towards entropy, otherwise known as chaos. Yet, on the next page it tells a story of a drop of dye in a container of clear water.

When the molecules of a dye are placed in water, the dye molecules move in various directions but their net movement is in a direction away from the concentrated source until every particle becomes eventually equally distributed throughout the container in a seemingly random way, and to the visible eye, the solution looks lightly evenly colored. The book also goes on to state how diffusion works. Molecules from an area of higher concentration move to an area of lesser concentration. No energy is required. It is spontaneous. The same thing goes for osmosis except with water, and since it takes no energy to perform these tasks, by definition they are working towards entropy.

However, with the rate of mutation and the bit error rate, also known to be effected by outside noise, or more specifically electromagnetic waves also known as radioactive frequencies, is it really so random after all?

If everything is going towards an equal distribution, a form of balance and equilibrium, is it really chaos?

I do not think that this is a form of chaos, but rather order, and random is obviously not so random after all. This would mean that everything is trying to become equally dispersed until a state of equilibrium is reached.

For example, If a bookshelf falls on the floor all the books fall from the bookshelf, in a seemingly random way; however, depending on how the bookshelf falls, how much force, tilt and direction, where the wind is, how much wind, the temperature of the room for the speed of the particles, add the gravity etc, and the books themselves and their properties, will determine where and how the books spread out throughout a room. Therefore becoming more evenly spaced apart or dispersed with a net movement away from the concentrated source of the bookshelf within the room and the known universe. It takes no or little energy for items in a room to become more equally distributed, but energy is needed to compact all those books back onto the shelf, or to compress clothes into a hamper, toys in a box, containers or shelves, or to condense clothes into drawers etc.