# 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 stars, 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)

# Oh My Guardian #8

“When it comes to Harry Potter, JK Rowling just can’t leave it alone. This is not necessarily a bad thing – fans have got to see Harry and friends all grown-up in the Cursed Child plays – but she’s also managed to muddy the waters by her constant rejigging of the original narrative furniture.” — Fantastic Beasts isn’t racist, but JK Rowling should stop tweaking the source material, Hannah Flint, The Guardian, 28ix2018.

Oh My Guardian #7 — the previous entry in this award-winning series
Reds under the Thread more on mixed metaphors… in terms of The Guardian
All posts interrogating issues around the Guardian-reading community and its affiliates

# Toxic Turntable #17

Currently listening…

• Gegozra, Musik für (2011)
• Billy Zais Foster, Red Hook (1962)
• Agavuel, Posla (1983)
• H7 Autobus, Unquietism (1977)
• C.M. Safie, Five Make Oblivion (1991)
• Duj Duj Bitumen, MuSekt (1998)
• Mir Toltor, Daub the Wood (1978)
• Über-Cseff, Ebe Dva (1996)
• Zue Aqhu, Vol. III (2013)
• Opus Pente, Nixed (1994)
• Aol Yie, Haaol (1982)
• Qizaia+, Glidepath (2008)
• X-Flower, Surciam Goba (2013)
• Lesley Hackett, Benjamin Said (1989)
• Zouque, Equinoctis (1989)
• Ludwig Abeille, Piano Concerto in D-major (2003)
• Les Mains Magiques, Hysteriac Celeriac (1975)

Previously pre-posted:

Toxic Turntable #1#2#3#4#5#6#7#8#9#10#11#12#13#14#15#16 •