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)


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

Bird Up!


Carolina Parrot from Birds of America by John James Audubon (1785-1851)

(click for larger)


Also known as the Carolina parakeet, Conuropsis carolinensis, this bird is now extinct.