# Fractal + Star = Fractar

Here’s a three-armed star made with three lines radiating at intervals of 120°: Triangular fractal stage #1

At the end of each of the three lines, add three more lines at half the length: Triangular fractal #2

And continue like this: Triangular fractal #3 Triangular fractal #4 Triangular fractal #5 Triangular fractal #6 Triangular fractal #7 Triangular fractal #8 Triangular fractal #9 Triangular fractal #10 Triangular fractal (animated)

Because this fractal is created from a series of star, you could call it a fractar. Here’s a black-and-white version: Triangular fractar (black-and-white) Triangular fractar (black-and-white) (animated)
(Open in a new window for larger version if the image seems distorted)

A four-armed star doesn’t yield an easily recognizable fractal in a similar way, so let’s try a five-armed star: Pentagonal fractar stage #1 Pentagonal fractar #2 Pentagonal fractar #3 Pentagonal fractar #4 Pentagonal fractar #5 Pentagonal fractar #6 Pentagonal fractar #7 Pentagonal fractar (animated) Pentagonal fractar (black-and-white) Pentagonal fractar (bw) (animated)

And here’s a six-armed star: Hexagonal fractar stage #1 Hexagonal fractar #2 Hexagonal fractar #3 Hexagonal fractar #4 Hexagonal fractar #5 Hexagonal fractar #6 Hexagonal fractar (animated) Hexagonal fractar (black-and-white) Hexagonal fractar (bw) (animated)

And here’s what happens to the triangular fractar when the new lines are rotated by 60°: Triangular fractar (60° rotation) #1 Triangular fractar (60°) #2 Triangular fractar (60°) #3 Triangular fractar (60°) #4 Triangular fractar (60°) #5 Triangular fractar (60°) #6 Triangular fractar (60°) #7 Triangular fractar (60°) #8 Triangular fractar (60°) #9 Triangular fractar (60°) (animated) Triangular fractar (60°) (black-and-white) Triangular fractar (60°) (bw) (animated) Triangular fractar (60°) (no lines) (black-and-white)

A four-armed star yields a recognizable fractal when the rotation is 45°: Square fractar (45°) #1 Square fractar (45°) #2 Square fractar (45°) #3 Square fractar (45°) #4 Square fractar (45°) #5 Square fractar (45°) #6 Square fractar (45°) #7 Square fractar (45°) #8 Square fractar (45°) (animated) Square fractar (45°) (black-and-white) Square fractar (45°) (bw) (animated)

Without the lines, the final fractar looks like the plan of a castle: Square fractar (45°) (bw) (no lines)

And here’s a five-armed star with new lines rotated at 36°: Pentagonal fractar (36°) #1 Pentagonal fractar (36°) #2 Pentagonal fractar (36°) #3 Pentagonal fractar (36°) #4 Pentagonal fractar (36°) #5 Pentagonal fractar (36°) #6 Pentagonal fractar (36°) #7 Pentagonal fractar (36°) (animated)

Again, the final fractar without lines looks like the plan of a castle: Pentagonal fractar (36°) (no lines) (black-and-white)

Finally, here’s a six-armed star with new lines rotated at 30°: Hexagonal fractar (30°) #1 Hexagonal fractar (30°) #2 Hexagonal fractar (30°) #3 Hexagonal fractar (30°) #4 Hexagonal fractar (30°) #5 Hexagonal fractar (30°) #6 Hexagonal fractar (30°) (animated)

And the hexagonal castle plan: Hexagonal fractar (30°) (black-and-white) (no lines)