This Means RaWaR

The Overlord of the Über-Feral says: Welcome to my bijou bloguette. You can scroll down to sample more or simply:

• Read a Writerization at Random: RaWaR


• O.o.t.Ü.-F.: More Maverick than a Monkey-Munching Mingrelian Myrmecologist Marinated in Mescaline…

• ¿And What Doth It Mean To Be Flesh?

მათემატიკა მსოფლიოს მეფე


*Der Muntsch ist Etwas, das überwunden werden soll.

Mullennial Mysterium

Mull (island) Arg. Malaios c. 150. Pre-Celtic island name. (The Oxford Dictionary of British Place Names)


Elsewhere other-engageable:

Place of Glades — a review of The Oxford Dictionary of British Place Names, A.D. Mills (1991)

Binary Babushkas

What’s the connection between grandmothers and this set of numbers?


1, 2, 6, 12, 44, 92, 184, 1208, 1256, 4792, 9912, 19832, 39664, 563952, 576464, 4496112, 4499184, 17996528, 17997488, 143972080, 145057520, 145070832, 294967024, 589944560...

To take the first step towards the answer, you need to put the numbers into binary:


1, 10, 110, 1100, 101100, 1011100, 10111000, 10010111000, 10011101000, 1001010111000, 10011010111000, 100110101111000, 1001101011110000, 10001001101011110000, 10001100101111010000, 10001001001101011110000, 10001001010011011110000, 1000100101001101011110000, 1000100101001111010110000, 1000100101001101011011110000, 1000101001010110011011110000, 1000101001011001101011110000, 10001100101001101011011110000, 100011001010011101011011110000...

The second step is compare those binary numbers with these binary numbers, which represent 1 to 30:


1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110...

To see what’s going on, take the first five numbers from each set:


• 1, 10, 110, 1100, 101100...
• 1, 10, 11, 100, 101...

What’s going on? If you look, you can see the n-th binary number of set 1 contains the digits of all binary numbers <= n in set 2. For example, 101100 is the 5th binary number in set 1, so it contains the digits of the binary numbers 1 to 5:


101100 ← 1
101100 ← 10
101100 ← 11
101100 ← 100
101100 ← 101

Now try 1256 = 10,011,101,000, the ninth number in set 1. It contains all the binary numbers from 1 to 1001:


10011101000 ← 1 (n=1)
10011101000 ← 10 (n=2)
10011101000 ← 11 (n=3)
10011101000 ← 100 (n=4)
10011101000 ← 101 (n=5)
10011101000 ← 110 (n=6)
10011101000 ← 111 (n=7)
10011101000 ← 1000 (n=8)
10011101000 ← 1001 (n=9)

But where do grandmothers come in? They come in via this famous toy:

Nested doll or Russian doll

It’s called a Russian doll and the way all the smaller dolls pack inside the largest doll reminds me of the way all the smaller numbers 1 to 1010 pack into 1001010111000. But in the Russian language, as you might expect, Russian dolls aren’t called Russian dolls. Instead, they’re called matryoshki (матрёшки, singular матрёшка), meaning “little matrons”. However, there’s a mistaken idea in English that in Russian they’re called babushka dolls, from Russian бабушка, babuška, meaning “grandmother”. And that’s what I thought, until I did a little research.

But the mistake is there, so I’ll call these babushka numbers or grandmother numbers:


1, 2, 6, 12, 44, 92, 184, 1208, 1256, 4792, 9912, 19832, 39664, 563952, 576464, 4496112, 4499184, 17996528, 17997488, 143972080, 145057520, 145070832, 294967024, 589944560...

They’re sequence A261467 at the Online Encyclopedia of Integer Sequences. They go on for ever, but the biggest known so far is 589,944,560 = 100,011,001,010,011,101,011,011,110,000 in binary. And here is that binary babushka with its binary babies:


100011001010011101011011110000 ← 1 (n=1)
100011001010011101011011110000 ← 10 (n=2)
100011001010011101011011110000 ← 11 (n=3)
100011001010011101011011110000 ← 100 (n=4)
100011001010011101011011110000 ← 101 (n=5)
100011001010011101011011110000 ← 110 (n=6)
100011001010011101011011110000 ← 111 (n=7)
100011001010011101011011110000 ← 1000 (n=8)
100011001010011101011011110000 ← 1001 (n=9)
100011001010011101011011110000 ← 1010 (n=10)
100011001010011101011011110000 ← 1011 (n=11)
100011001010011101011011110000 ← 1100 (n=12)
100011001010011101011011110000 ← 1101 (n=13)
100011001010011101011011110000 ← 1110 (n=14)
100011001010011101011011110000 ← 1111 (n=15)
100011001010011101011011110000 ← 10000 (n=16)
100011001010011101011011110000 ← 10001 (n=17)
100011001010011101011011110000 ← 10010 (n=18)
100011001010011101011011110000 ← 10011 (n=19)
100011001010011101011011110000 ← 10100 (n=20)
100011001010011101011011110000 ← 10101 (n=21)
100011001010011101011011110000 ← 10110 (n=22)
100011001010011101011011110000 ← 10111 (n=23)
100011001010011101011011110000 ← 11000 (n=24)
100011001010011101011011110000 ← 11001 (n=25)
100011001010011101011011110000 ← 11010 (n=26)
100011001010011101011011110000 ← 11011 (n=27)
100011001010011101011011110000 ← 11100 (n=28)
100011001010011101011011110000 ← 11101 (n=29)
100011001010011101011011110000 ← 11110 (n=30)

Babushka numbers exist in higher bases, of course. Here are the first thirteen in base 3 or ternary:


1 contains 1 (c=1) (n=1)
12 contains 1, 2 (c=2) (n=5)
102 contains 1, 2, 10 (c=3) (n=11)
1102 contains 1, 2, 10, 11 (c=4) (n=38)
10112 contains 1, 2, 10, 11, 12 (c=5) (n=95)
101120 contains 1, 2, 10, 11, 12, 20 (c=6) (n=285)
1021120 contains 1, 2, 10, 11, 12, 20, 21 (c=7) (n=933)
10211220 contains 1, 2, 10, 11, 12, 20, 21, 22 (c=8) (n=2805)
100211220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100 (c=9) (n=7179)
10021011220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100, 101 (c=10) (n=64284)
1001010211220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102 (c=11) (n=553929)
1001011021220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110 (c=12) (n=554253)
10010111021220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111 (c=13) (n=1663062)

Look at 1,001,010,211,220 (n=553929) and 1,001,011,021,220 (n=554253). They have the same number of digits, but the babushka 1,001,011,021,220 manages to pack in one more baby:


1001010211220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102 (c=11) (n=553929)
1001011021220 contains 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110 (c=12) (n=554253)

That happens in binary too:


10010111000 contains 1, 10, 11, 100, 101, 110, 111, 1000, 1001 (c=9) (n=1208)
10011101000 contains 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010 (c=10) (n=1256)

What happens in higher bases? Watch this space.

Performativizing Papyrocentricity #67

Papyrocentric Performativity Presents:

Early RiserDecline and Fall, Evelyn Waugh (1928)

The Future is FascistFuturism, Richard Humphreys (1999 Tate Publishing)

Mystery and MeaningDictionary of Plant Names, Allen J. Coombes (1985)

Noshing on NoxiousnessNekro-Noxious: Toxic Tales of True Transgression in Miami Municipal Mortuary, Norberto Fetidescu (TransVisceral Books 2018)


Or Read a Review at Random: RaRaR

Go Too Woke on an Egg

Goop to pay out over unproven health benefits of vaginal eggs

Goop, the new age lifestyle and publishing company founded by the [actress] Gwyneth Paltrow, has agreed to pay a substantial settlement over unproven claims about the health benefits of its infamous vaginal eggs. Goop’s website still claims that inserting the eggs into the vagina helps “cultivate sexual energy, clear chi pathways in the body, intensify femininity, and invigorate our life force”.

Its $66 Jade Egg and $55 Rose Quartz egg are still offered for sale on the site, but the company has agreed to pay $145,000 to settle allegations that it previously made unscientific claims about the eggs, and a herbal essence that it had said helped tackle depression.

It also agreed to refund customers who purchased the products from January to August last year. During that period it claimed the eggs could balance hormones, regulate menstrual cycles, prevent uterine prolapse, and increase bladder control, according to officials in Santa Clara part of a group of California district attorneys who filed the lawsuit. — Goop to pay out over unproven health benefits of vaginal eggs, The Guardian, 5ix2018.


N.B. The title of this incendiary intervention is a paronomasia on the old British advertising slogan “Go to work on an egg.”

Capnic Caravan

Sleep, Dopesmoker (2012 reissue)


I’ve never been able to get into the band Sleep and, not being a keyly committed core component of the hive-mind, I’m not a fan of dopesmoking either. But this is a good cover by the artist Arik Roper, with a nice Dune-y vibe.


To engage issues around the title of this incendiary intervention, see here:

capno-, capn-, capnod- (Greek: smoke; vapor; sooty) — Wordquests

The Hum of Heresy

I don’t know any exceptions to the rule that someone who likes William Burroughs will also be a member in terms of core issues around the hive-mind. From Kurt Cobain to Will Self: if you get a buzz outa Burroughs, that won’t be the only buzzing you’re corely acquaintanced with… And I predict that you’ll frequently use, hear and read core items from the hive-mind term-set such as “in terms of”, “prior to”, “issues around”, “engagement with”, “spike”, “skill-set”, “core”, “key”, “toxic” and “edgy”… You’ll also like italics and trailing dots

“There was a certain edgy excitement to turning on the computer every morning and immediately checking to see what Mark had thrown down in terms of an ideas-gauntlet.” – Simon Reynolds in the foreword to K-Punk: The Collected and Unpublished Writings of Mark Fisher (2004–2016), edited by Darren Ambrose, Repeater Books 2018.


Elsewhere other-engageable:

Ex-term-in-ate!
Don’t Do Dot…
Prior Analytics
Spike-U-Like?

Back to Drac’

draconic, adj. /drəˈkɒnɪk/ pertaining to, or of the nature of, a dragon. [Latin draco, -ōnem, < Greek δράκων dragon] — The Oxford English Dictionary

In Curvous Energy, I looked at the strange, beautiful and complex fractal known as the dragon curve and showed how it can be created from a staid and sedentary square:

A dragon curve


Here are the stages whereby the dragon curve is created from a square. Note how each square at one stage generates a pair of further squares at the next stage:

Dragon curve from squares #1


Dragon curve from squares #2


Dragon curve from squares #3


Dragon curve from squares #4


Dragon curve from squares #5


Dragon curve from squares #6


Dragon curve from squares #7


Dragon curve from squares #8


Dragon curve from squares #9


Dragon curve from squares #10


Dragon curve from squares #11


Dragon curve from squares #12


Dragon curve from squares #13


Dragon curve from squares #14


Dragon curve from squares (animated)


The construction is very easy and there’s no tricky trigonometry, because you can use the vertices and sides of each old square to generate the vertices of the two new squares. But what happens if you use lines rather than squares to generate the dragon curve? You’ll discover that less is more:

Dragon curve from lines #1


Dragon curve from lines #2


Dragon curve from lines #3


Dragon curve from lines #4


Dragon curve from lines #5


Each line at one stage generates a pair of further lines at the next stage, but there’s no simple way to use the original line to generate the new ones. You have to use trigonometry and set the new lines at 45° to the old one. You also have to shrink the new lines by a fixed amount, 1/√2 = 0·70710678118654752… Here are further stages:

Dragon curve from lines #6


Dragon curve from lines #7


Dragon curve from lines #8


Dragon curve from lines #9


Dragon curve from lines #10


Dragon curve from lines #11


Dragon curve from lines #12


Dragon curve from lines #13


Dragon curve from lines #14


Dragon curve from lines (animated)


But once you have a program that can adjust the new lines, you can experiment with new angles. Here’s a dragon curve in which one new line is at an angle of 10°, while the other remains at 45° (after which the full shape is rotated by 180° because it looks better that way):

Dragon curve 10° and 45°


Dragon curve 10° and 45° (animated)


Dragon curve 10° and 45° (coloured)


Here are more examples of dragon curves generated with one line at 45° and the other line at a different angle:

Dragon curve 65°


Dragon curve 65° (anim)


Dragon curve 65° (col)


Dragon curve 80°


Dragon curve 80° (anim)


Dragon curve 80° (col)


Dragon curve 135°


Dragon curve 135° (anim)


Dragon curve 250°


Dragon curve 250° (anim)


Dragon curve 250° (col)


Dragon curve 260°


Dragon curve 260° (anim)


Dragon curve 260° (col)


Dragon curve 340°


Dragon curve 340° (anim)


Dragon curve 340° (col)


Dragon curve 240° and 20°


Dragon curve 240° and 20° (anim)


Dragon curve 240° and 20° (col)


Dragon curve various angles (anim)


Previously pre-posted:

Curvous Energy — a first look at dragon curves

Toxic Turntable #16

Currently listening…

• Kev Neuys, Eloquence Foss (1964)
• Zetic Load, Loadstar (1991)
• Vi Jubilatus, Quinconce EP (1979)
• Ylikipojga, Vazhwevac Xviwv (1991)
• Voïde Thyroïde, I by the Yellow Door (1996)
• Weepster, Glows the Ghost (1983)
• Nous les Revenants, L’Iodisme (1988)
• Jiji è Vgelu, Live in Rheims (2016)
• Hex Dwi, Cats is Simplicity (1994)
• Quixotic Plovers, Imagine Us (2006)
• Rantique + Mizao, Oklahama + Ecclesia Sanctorum (split EP) (2008)
• Elizabeth Dobie, Uppers/Downers (1981)
• Zed Follows Wye, Goats in Etruria (2000)
• Hyssop-773, Abeoma (1987)
• Francesco Manfredini, 12 Concerti (1997)
• Eark, Xeno-Zoo (1993)


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

Rigging in the Trigging

Here’s a simple pattern of three triangles:

Three-Triangle Pattern


Now replace each triangle in the pattern with the same pattern at a smaller scale:

Replacing triangles


If you keep on doing this, you create what I’ll call a trigonal fractal (trigon is Greek for “triangle”):

Trigonal Fractal stage #3 (click for larger)


Trigonal Fractal stage #4


Trigonal Fractal stage #5


Trigonal Fractal #6


Trigonal Fractal #7


Trigonal Fractal #8


Trigonal Fractal (animated) (click for larger)


You can use the same pattern to create different fractals by rotating the replacement patterns in different ways. I call this “rigging the trigging” and here are some of the results:




You can also use a different seed-pattern to create the fractals:

Trigonal fractal (animated)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)



Trigonal fractal (anim)


Note: The title of this incendiary intervention is of course a paronomasia on the song “Frigging in the Rigging”, also known as “Good Ship Venus” and performed by the Sex Pistols on The Great Rock ’n’ Roll Swindle (1979).