The logistic map is a mathematical model used to describe the population growth of a species over time. It is a simple equation that takes into account the effects of limited resources and environmental factors on population growth. The logistic map produces a pattern of population growth that exhibits chaotic behavior as the values of the model's parameters change, making it a valuable tool for studying complex systems.

The Buddhabrot fractal is a type of fractal that is generated by plotting the paths of points that escape from the Mandelbrot set. The resulting image resembles a series of intertwined spirals and branches, and is named after the shape it resembles, which is said to resemble the seated figure of Buddha. The Buddhabrot fractal is created by assigning each point in the complex plane a "color" based on how many times it takes for that point to escape from the Mandelbrot set, and then plotting the paths of the points that do escape. This process is repeated millions of times, resulting in a highly detailed and intricate fractal image.

The Barnsley Fern is a fractal pattern named after British mathematician Michael Barnsley. It is generated by an iterative process that involves repeatedly applying a set of geometric transformations to a simple initial shape. The resulting fern-like pattern displays self-similarity at different scales, and has applications in computer graphics, image compression, and chaos theory.