Toxic Turntable #11

Currently listening…

• Watchful Hags, Snakes of Grace (1996)
• Jupiter Pore, Gneumos (1980)
• Sixmith, Internecine (2010)
• The Hext, Celestial Chimes (1982)
• Why We Wander, W3 E.P. (1986)
• Zoön, Zoönotic Rhythms (2011)
• Fen Witches, Wild Hunt (1998)
• Virolator, V-003 (2014)
• Slow Exploding Gulls, Yr Wylan Ddu (2003)
• Doris Day, The Best Of… (1987)
• Sirium, MoCoT (2013)

Previously pre-posted:

Toxic Turntable #1#2#3#4#5#6#7#8#9#10

Jumper to Jumper

Previously I’ve looked at fractals created by a point moving half-way towards the random chosen vertex of a polygon. But you can also choose an initial vertex, then choose a new vertex by adding a random number to that initial vertex. Then repeat. For example, if the polygon is a square and the initial vertex is v = 1, then choose v + 3 = 4 or v – 1 = 3, and so on.

You can then ban or un-ban the choice of vertex-jump as you can ban or un-ban direct choices of vertex. These two methods of random choice are effectively the same, but one can be simpler to program than the other. That’s why I’ve come across some new fractals by using vertex-jumps. Here they are:

vertices = 4, vertex-jump = (1,2,3,4), ban on same choice twice in a row

vertices = 4, vertex-jump = (1,2,3,4), ban on 2 in row (black-and-white version)

v = 4, vj = (1,2,3,4), ban on choice c + 2 from previous choice c

v = 4, vj = (1,2,3,4), ban c + 2 (animated gif)

vj = (1,2,3,4), ban c + 2 (black-and-white)

vj = (1,2,3,4), ban c + 0 at time t+1 unless c + 0 at time t-1

vj = (1,2,3,4), ban c + 0 at t+1, unless c + 0 at t-1 (black-and-white)

vj = (1,2,3,4,5), ban c + 0

vj = (0,1,2,3,4), ban c + 0

vj = (0,1,2,3,4), ban c + 0 (black-and-white)

vj = (1,2,3,4), ban c + 2 at t+1 unless c + 2 at t-1 (animated gif)

vj = (1,2,3,4), ban c + various at t+1 unless c + various at t-1 (animated gif)

vj = (1,2,3,4,5), ban c + 0 at t+1 unless c + 0 at t-1

vj = (-2,-1,0,1,2), ban c + 0

vj = (-2,-1,0,1,2), ban c + 0 (black-and-white)

vj = (0,1,2,3,4), ban c + va unless c + va

v = 5, vj = (1,2,3,4), ban c + 0

v = 5, vj = (1,2,3,4), ban c + 2

v = 5, vj = (0,1,2,3), ban c + 3

v = 6, vj = (0,1,2,3), ban c + 2

v = 6, vj = va, ban c + va (animated gif)

Are U Worthy?

If you’re nagged by doubts as to whether you really are a keyly committed core component of the counter-cultural community, then simply engage issues around the following issues…

1. In terms of “in terms of”, how often do you hear this phantasmagoric phrase in terms of a daily basis?

2. Please hierarchialize the following core components of the counter-cultural icon community in terms of their “in-terms-of”-usage metrics: Will Self, J.G. Ballard, William Burroughs, Alan Moore, Miriam Stimbers, Michael Moorcock, Kathy Acker, Genesis P. Orridge, Alan Ginsberg, Stewart Home, Hubert Selby Jr., Norman Foreman (B.A.). (I.e., if you think Foreman uses “in terms of” most in terms of usage metrics, put him first; if you think Acker uses it second-most, put her second; etc.)

3. Engage issues around 1 and 2 again, replacing “in terms of” with “prior to”…

4. Engage issues around 1 and 2 again, replacing “in terms of” with “issues around”……

5. Engage issues around 1 and 2 again, replacing “in terms of” with “Vote Corbyn”………

Once you’ve engaged issues around the above issues, email your answers to Evaluator!@NakedKrunch and you should have your doubts laid to rest within 23 working days…

Previously pre-posted on Overlord of the Über-Feral…

Les Sez
Don’t Do Dot…
Metricizing Michael…
Terminal Breach
More Termination…

Sphere Hear

οὐσίαν θεοῦ σφαιροειδῆ, μηδὲν ὅμοιον ἔχουσαν ἀνθρώπωι· ὅλον δὲ ὁρᾶν καὶ ὅλον ἀκούειν, μὴ μέντοι ἀναπνεῖν· σύμπαντά τε εἶναι νοῦν καὶ φρόνησιν καὶ ἀίδιον. — Διογένης Λαέρτιος, Βίοι καὶ γνῶμαι τῶν ἐν φιλοσοφίᾳ εὐδοκιμησάντων

    “The substance of God is spherical, in no way resembling man. He is all eye and all ear, but does not breathe; he is the totality of mind and thought, and is eternal.” — Xenophanes’ concept of God in Diogenes Laërtius’ Lives of Eminent Philosophers (c. 280-320 AD), Book IX, chapter 2 (translated by R.D. Hicks, 1925)

Appointment with Distality

distal, adj. Anat. Situated away from the centre of the body, or from the point of origin (said of the extremity or distant part of a limb or organ); terminal. Opp. to proximal. [← stem of dist- (in distant adj.) + -al, after dorsal, ventral, etc.] — Oxford English Dictionary

When a point jumps inside a triangle, moving halfway towards a randomly chosen vertex each time, a fractal known as the Sierpiński triangle appears:

Point jumping halfway towards random vertex of a triangle


Point jumping inside triangle (black-and-white version)

But when a point moves at random in the same way inside a square, no fractal appears. Instead, the interior of the square gradually fills with a haze of pixels:

Point jumping halfway towards random vertex of a square

Now trying imposing restrictions on the point jumping inside a square. If it can’t jump towards a vertex twice in a row, this fractal appears:

Ban consecutive jumps towards same vertex


Ban consecutive jumps towards same vertex (black-and-white version)

Suppose the vertices are numbered from 1 to 4 and the point can’t jump towards the vertex one lower than the previously chosen vertex. That is, if it jumps towards vertex 3, it can’t jump next towards vertex 2, but it can jump towards vertices 1, 3, or 4 (if the vertex is 1, it’s banned from moving towards vertex 4, i.e. 1-1 = 0 = 4). Now this fractal appears:

Ban jump towards vertex v-1


This is the fractal when the point can’t jump towards the vertex two places lower than the one it has just jumped towards:

Ban jump towards vertex v-2


But if you can ban, you can also un-ban. Suppose the point jumps towards vertex v at time t and is then banned from jumping towards vertex v-2 at time t+1 unless it had jumped towards vertex v-1 at time t-1. This interesting fractal appears:

Ban jump v-2 at t+1 unless jump v-1 at t-1

Here are some more fractals using the ban / un-ban technique:

Ban / un-ban various


Ban jump v+0 at t+1 unless jump v+1 at t-1


Ban jump v+1 at t+1 unless jump v+3 at t-1


Ban jump v+0 at t+1 unless jump v+2 at t-1


Ban jump v+2 at t+1 unless jump v+2 at t-1


Ban / un-ban various

You can also impose or lift bans based not on the vertex the point jumps towards, but on the distance the point jumps. For example, take the radius r of the circle circumscribing the square and divide it into four segments, 0 to ¼r, ¼r to ½r, ½r to ¾r, and ¾r to r. When the point is going to jump towards vertex v, test whether its jump will land in the same segment, measured from the center of the circle, as it currently occupies. If it does, ban the jump and choose another vertex. Or unban the vertex if the point occupied segment s + x at time t-1. Here are some of the fractals produced using this technique:

Ban / un-ban based on distance jumped


Ban jump into segment s+0 of 4


Ban jump into segment s+1 from center


Ban jump into segment s+2


Ban jump into s+2 at t+1 unless jump into s+2 at at t-1


Ban jump into s+0 from present point


Ban jump into s+2 from present point


Ban jump into s+3 from present point


Ban jump into s+0 at t+1 unless jump into s+1 at at t-1

It’s easy to think of variants on all these themes, but I’ll leave them as an exercise for the interested reader.