This unusual shaped afghan is based on the Golden Mean and the Fibonacci Sequence.
The shape is known as the Golden Spiral.
The Golden Mean is special ratio which has been used widely, around the world, for thousands of years, in art and design. It also occurs very often in nature. Items using these proportions ‘look right’ to most people.
Adding the border means that the proportions of the completed afghan are not quite those of the Golden Mean. If you want to maintain mathematical accuracy you can omit the border or mount the spiral on a rectangle of fabric or crochet, as described in the instructions.
It is very easy to making using crochet trebles throughout (UK definition). Only basic crochet skills are needed.
The afghan in the photos was made in DK yarns. It could be made in any yarn though this would change the overall size.
The instructions also contain several variations for more complex use of spirals. Another possibility is to omit the largest sections to create a pillow or wall-hanging.