Toxic Turntable #13

Currently listening…

• Ilm Beogdé, Best Of (1994)
• The Brandywines, Ludlow (1988)
• Murine, A Glass Alga (1997)
• Ichtherion, Et Agnus Vincet (1975)
• Xmode, Giftzwerg (1982)
• Uar Csolt, Marginsur (2010)
• Thomas Skinner Orchestra, Wasidu (1959)
• Elxuve, Howdja (1991)
• Iwri, Iwri 2 (1979)
• Henkerkunst, Gänzehaut (2011)
• Albion Chimes, Soltrip (1969)
• Vihol, F.E.S. (1982)
• Aitmao w Niau, Celebes (2012)


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

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Bats and Butterflies

I’ve used butterfly-images to create fractals. Now I’ve found a butterfly-image in a fractal. The exciting story begins with a triabolo, or shape created from three isoceles right triangles:


The triabolo is a rep-tile, or shape that can be divided into smaller copies of itself:


In this case, it’s a rep-9 rep-tile, divisible into nine smaller copies of itself. And each copy can be divided in turn:


But what happens when you sub-divide, then discard copies? A fractal happens:

Fractal crosses (animated)


Fractal crosses (static)


That’s a simple example; here is a more complex one:

Fractal butterflies #1


Fractal butterflies #2


Fractal butterflies #3


Fractal butterflies #4


Fractal butterflies #5


Fractal butterflies (animated)


Some of the gaps in the fractal look like butterflies (or maybe large moths). And each butterfly is escorted by four smaller butterflies. Another fractal has gaps that look like bats escorted by smaller bats:

Fractal bats (animated)

Fractal bats (static)


Elsewhere other-posted:

Gif Me Lepidoptera — fractals using butterflies
Holey Trimmetry — more fractal crosses

Noise from Nowhere

• Es war, als ob er irgendwohin horchte, auf irgend ein unheimliches Geräusch. — Thomas Mann, Der kleine Herr Friedemann (1897).

   • He seemed somehow to be listening, listening to some uncanny noise from nowhere. — Thomas Mann, “Little Herr Friedemann” (translated by David Luke).

Holey Trimmetry

Symmetry arising from symmetry isn’t surprising. But what about symmetry arising from asymmetry? You can find both among the rep-tiles, which are geometrical shapes that can be completely replaced by smaller copies of themselves. A square is a symmetrical rep-tile. It can be replaced by nine smaller copies of itself:

Rep-9 Square

If you trim the copies so that only five are left, you have a symmetrical seed for a symmetrical fractal:

Fractal cross stage #1


Fractal cross #2


Fractal cross #3


Fractal cross #4


Fractal cross #5


Fractal cross #6


Fractal cross (animated)


Fractal cross (static)


If you trim the copies so that six are left, you have another symmetrical seed for a symmetrical fractal:

Fractal Hex-Ring #1


Fractal Hex-Ring #2


Fractal Hex-Ring #3


Fractal Hex-Ring #4


Fractal Hex-Ring #5


Fractal Hex-Ring #6


Fractal Hex-Ring (animated)


Fractal Hex-Ring (static)


Now here’s an asymmetrical rep-tile, a nonomino or shape created from nine squares joined edge-to-edge:

Nonomino


It can be divided into twelve smaller copies of itself, like this:

Rep-12 Nonomino (discovered by Erich Friedman)


If you trim the copies so that only five are left, you have an asymmetrical seed for a familiar symmetrical fractal:

Fractal cross stage #1


Fractal cross #2


Fractal cross #3


Fractal cross #4


Fractal cross #5


Fractal cross #6


Fractal cross (animated)


Fractal cross (static)


If you trim the copies so that six are left, you have an asymmetrical seed for another familiar symmetrical fractal:

Fractal Hex-Ring #1


Fractal Hex-Ring #2


Fractal Hex-Ring #3


Fractal Hex-Ring #4


Fractal Hex-Ring #5


Fractal Hex-Ring (animated)


Fractal Hex-Ring (static)


Elsewhere other-available:

Square Routes Re-Re-Visited

Games of Zones

The Badminton Game by David Inshaw

David Inshaw, The Badminton Game (1972-3)

I first came across this beautiful and mysterious painting in a book devoted to British art. Then I forgot the name of both artist and painting, and couldn’t get at the book any more. Years later, I’ve found it again on the cover of a paperback in a secondhand shop. I like the way it combines zones: the domestic and the dendric, the lunar and the ludic, the terrestrial and the celestial. And it’s full of fractals: the trees, the clouds and, implicitly, the moon and the two girls playing badminton.

Performativizing Papyrocentricity #58

Papyrocentric Performativity Presents:

Diamond in the DirtDirty Story: A further account of the life and adventures of Arthur Abdel Simpson, Eric Ambler (Bodley Head 1967)

Spin DoctorateGossamer Days: Spiders, Humans and Their Threads, Eleanor Morgan (Strange Attractor Press 2016)

Kid ChaosStill William, Richmal Crompton (1925)

Permission to BlandSomething Fresh, P.G. Wodehouse (1915)

Succulent Selections – for Sizzlingly Serebral Splanchnoscopophilists…

Tempting a Titan – a further exclusive extract from Titans of Transgression (TransVisceral Books, forthcoming)


• Or Read a Review at Random: RaRaR

He Say, He Sigh, He Sow #46

“… for comic effect he also drew on neglected Arabic words, including buldah, or ‘freedom from hair of the space between the eyebrows’, and bahsala, to ‘remove one’s clothes and gamble with them’.” — Christopher de Bellaigue, The Islamic Enlightenment: The Modern Struggle between Faith and Reason (2017), writing of the Lebanese Christian Maronite novelist Ahmad Faris al-Shidyaq (1805-87) (ch. 5, Vortex, pg. 167)

Bent for the Pent

A triangle can be tiled with triangles and a square with squares, but a pentagon can’t be tiled with pentagons. At least, not in the same way, using smaller copies of the same shape. The closest you can get is this:

Pentaflake #1


If you further subdivide the pentagon, you create what is known as a pentaflake:

Pentaflake #2


Pentaflake #3


Pentaflake #4


Pentaflake (animated)


Pentaflake (static)


But if you bend the rules and use irregular smaller pentagons, you can tile a pentagon like this, creating what I called a pentatile:

Pentatile stage 1


Further subdivisions create an interesting final pattern:

Pentatile #2


Pentatile #3


Pentatile #4


Pentatile #5


Pentatile #6


Pentatile (animated)


Pentatile (static)


By varying the size of the central pentagon, you can create other patterns:

Pentatile #1 (animated)


Pentatile #2 (animated)

Pentatile #2







Pentatile with no central pentagon


And here are various pentatiles in an animated gif:


And here are some variations on the pentaflake:







Elsewhere other-posted:

Bent for the Rent (1976) — the title of the incendiary intervention above is of course a reference to the “first and last glitter-rock album” by England’s loudest band, Spinal In Terms Of Tap
Phrallic Frolics — more on pentaflakes