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


• ¿And What Doth It Mean To Be Flesh?

მათემატიკა მსოფლიოს მეფე


Gweel & Other Alterities – Incunabula’s new edition


Tales of Silence & Sortilege – Incunabula’s new edition



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Hopping in Boundland

Shopping in Poundland. That’s what Brits do when they want cheap fills. Hopping in Boundland. That’s what rec-mathers do when they want deep thrills. As I’ve described previously, a point can create interesting geometry by jumping towards fixed vertices inside a polygon. But it can also create interesting geometry by jumping at fixed angles inside a polygon. Suppose a point jumps at 0°, 120° or 240° halfway towards the perimeter of a triangle. It’s bounded in its jumps, so you could say it’s hopping in Boundland. Or bounding in Hopland. Either way, it creates this pattern inside the polygon:

Jumping halfway towards perimeter of triangle at 0°, 120° or 240°


If you stretch the triangle-and-pattern into a circle, you get this (the graphics aren’t as good as they could be, but I’m working on it):

Triangle → circle, 1/2 at 0°, 120° or 240°


You can also introduce restrictions, like banning the point from jumping at the same angle twice in a row:

Ban on same angle twice in a row, 1/2 jump at 0°, 120° or 240°


Triangle → circle, ban j+0, 1/2 jump at 0°, 120° or 240°


If the jump is 2/3rds of the distance to the perimeter and the ban is on the same angle twice, the point generates this pattern by hopping in Boundland:

Triangle, 2/3 jump, ban j+0, 0°, 120° or 240°


Triangle → circle, 2/3 jump, ban j+0, 0°, 120° or 240°


Now try adjusting the angles. Swinging the angles 60° with the same 2/3rd jump and same ban, the point generates this:

Triangle, 2/3 jump, ban j+0, 60°, 180° or 300°


Triangle → circle, 2/3 jump, ban j+0, 60°, 180° or 300°


A point jumping 2/3rds at four angles inside a square generates this pattern:

Square, 2/3 jump, ban j+0, 45°, 135°, 225, 315°


Square → circle, 2/3 jump, ban j+0, 45°, 135°, 225, 315°


And what if the point jumps 5/7ths towards the center of the polygon, not just towards the perimeter? Then it generates this pattern inside a hexagon with a ban on jumping towards the angle adjacent clockwise to the angle it’s just jumped at:

Hexagon, 5/7 jump, ban j+1, 6 angles + center


The point can also jump inside a circle rather than a polygon. Here’s the pattern generating by a point jumping 2/3rds at three angles with a ban on the same jump twice in a row:

Circle, 2/3 jump, ban j+0, 3 angles


And if the point can jump towards the center of the circle too, it generates this pattern:

Circle, 2/3 jump, ban j+0, 3 angles + center


Elsewhere Other-Accessible

Controlled Chaos — a look at points jumping towards vertices, not perimeters

Nōmina Nūmina

M3FB.

My three favorite bands (or recording artists).

I can’t name them. I just can’t.

Okay, three names leap into my mind whenever I think about M3FB…

The Clash… Guns’n’Roses… Oasis…

But just because they leap doesn’t mean they really are M3FB. I mean, they are among my favorite bands, yes, obviously, or they wouldn’t leap in the first place.

But as soon as they’ve leapt, my brain starts clamoring: “What about Tupac? Sunn O)))? Iron Maiden? Bruce Springsteen? Prince? Huh? Not to mention [blah blah blah]”

So I just can’t do it.

I can’t name M3FB.

But.

M3FBN?

My three favorite band names?

Now you’re talking.

I can name M3FBN in an instant. And all my brain does is nod twice and say nowt.

So here they are, from simplest (and maybe cleverest) to poetickest:

The The
Photographed by Lightning
Rosa Voragine Submersa

Unfortunately, only one of the bands lives up to the cleverness and strangeness of its name. But in a way that’s good too. In some ways, it’s better to imagine what this album might sound like than hear music that in any way lived up to the words:

Renaissance D’Un Pétale Séché by Rosa Voragine Submersa

1. Renaissance D’Un Pétale Séché 06:46
2. Souviens-Toi Des Temps Anciens 04:03
3. Un Endroit Pour Eternel Repos 06:02
4. La Lune Esseulée 07:22
5. Les Meurtrissures D’Un Eté 03:42
6. Le Conte De La Muse Endormie 06:38
7. Par Delà Le Miroir, De L’Autre Côté Des Songes 08:52
8. La Valse Du Chloroforme 04:46
9. La Nébuleuse De L’Hiver – La Compagnie D’Un Prince Fantasmagorique 06:40
10. La Pantomime De L’Affliction 06:19
11. Un Endroit Pour Eternel Repos (version piano) 06:03
12. La Valse Du Chloroforme (version originale) 03:06
13. Renaissance D’Un Pétale Séché (version originale) 07:03

Renaissance D’Un Pétale Séché (free at Bandcamp)

She Terms Me On…

Racism and sexism have become normalised in Britain, the equalities minister has said, as she warned that young men were being sucked into violent misogyny by the “cesspit” of social media. Bridget Phillipson said she was increasingly worried about how commonplace misogyny and racism had become, fuelled by online interactions and statements by politicians she said would not have been acceptable a few years ago. […]

Speaking to the Guardian’s Politics Weekly podcast, she said: “I worry that we are at kind of a ground zero in terms of attitudes around violence against women and girls. Things that not very long ago felt totally unacceptable are becoming normal. I think we’re seeing that in terms of attitudes towards women, and I think we see that in terms of attitudes around racism.” […] The women and equalities minister also criticised the police for not taking violence against women and girls seriously enough. “We’ve seen some pretty shocking failings in terms of the police response over decades and sadly we’re not seeing the progress that we should in terms of how the police will often respond to this,” she said. — “Racism and sexism have become normalised in Britain, says equalities minister”, The Guardian, 20th in-terms-of August, 2026

Official portrait of Bridget Phillipson, 2026


Tony Blair by Steve Bell


John, I’m only dancing;
She turns me on, but I’m only dancing;
She turns me on, don’t get me wrong:
I’m only dancing — “John, I’m Only Dancing” (1972) by David in-terms-of-core Bowie

Angular Trerkel

Here’s the famous Sierpiński triangle, a fractal named after the Polish mathematician Wacław Sierpiński (1882-1969):

A Sierpiński triangle


You can create it by following all the possible paths of a point jumping half-way towards the vertices of the triangle. But what if the point can jump towards the center of the triangle too? Then you get another fractal, one that looks like this:

Sierpiński triangle when point can jump towards center of triangle too


Now, as a keyly committed core component of the trans-entitial community, I wondered whether triangles and triangular fractals might identify as other geometrical shapes…

I mean, what’s to stop a triangle identifying as a circle? Nothing. And obvs, if one of the Sierpiński triangles above identifies as a circle, it is a circle — trans-circles are circles (get over it). That is, there’s no need for Sierpiński surgery.

But what if a trans-circular Sierpiński triangle wanted to affirm its circularity with surgery? What would it look like then? Well, you can use elementary trig based on the angles of points within the triangle to stretch it into what might be called a trircle, i.e. a trans-circular triangle that has affirmed its inner circular identity:

A pre-op trans-circular Sierpiński triangle

🡇

A post-op trans-circular Sierpiński triangle or Sierpiński trircle


Sierpiński triangle → Sierpiński trircle (animated at EZgif)


On the other hand, the trircle might be a pre-op trans-triangular circle that has NOT affirmed its inner triangular identity with surgery. It’s complicated. But if we suppose it’s a post-op trans-circle rather than a pre-op trans-triangle, we could nickname it an Angular Trerkel, punning on the name of the great German Bundeskanzlerin Angela Merkel. Here’s the same Sierpiński surgery on the centered Sierpiński triangle (the second fractal looked at above):

A pre-op trans-circular centered Sierpiński triangle

🡇

A post-op trans-circular centered Sierpiński triangle or centered Sierpiński trircle


Centered Sierpiński triangle → centered Sierpiński trircle (animated at EZgif)


Again, the post-op trans-circular centered Sierpiński triangle might in fact be a pre-op trans-triangular centered Sierpiński circle. When it comes to the trans-entitial community, always remember: In dubio, interrogāte entitatem! — “In case of doubt, ask the entity!”

Cephalestial Schism

“To accept everything is an exercise, to understand everything a strain. The poet only desires exaltation and expansion, a world to stretch himself in. The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.” — G.K. Chesterton, Orthodoxy (1908)

Lūmen Nūmen

’Tis a green scene
With many white mouths:

The trumpet-mouths
Of bindweed

Begoddening
The sun-begoldened air.

And the hoverfly
To the fleabane’s eye

Sweets soft songs
I catch nor match.

Yet fleabane’s eye
To hoverfly:

Παντοπόρνη!

A Little Hextra


• 1, 2, 4, 8, 16, 31, 57, 99, 163, 256, 386, 562, 794, 1093, 1471, 1941, 2517, 3214, 4048, 5036, 6196, 7547, 9109, 10903, 12951, 15276, 17902, 20854, 24158, 27841, 31931, 36457, 41449, 46938, 52956, 59536, 66712, 74519, 82993, 92171, 102091, 112792, 124314, 136698 — A000127, “Maximal number of regions obtained by joining n points around a circle by straight lines”, at The Online Encyclopedia of Integer Sequences