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?
Gweel & Other Alterities – Incunabula’s new edition
Tales of Silence & Sortilege – Incunabula’s new edition
If you’d like to donate to O.o.t.Ü.-F., please click here.
I identify as √-37 (the square root of -37) in bases 5 (on Mondays and Wednesdays), 17 (Tuesdays, Thursdays and alternate Saturdays) and 89 (Fridays, Sundays and alternate Saturdays).
My preferred pronouns are 6.08276i, 雲 and მსოფლიოს მეფე.
To coin a phrase: Never Mind the Bollocks — Here’s the Hex Crystals! And what is a hex crystal? It’s what I call a shape that’s created algorithmo inside a hexagon and looks like a crystal:
A hex crystal
Here are some more hex-crystals:
I came across hex-crystals when I was looking at an interesting little geometrical question. How does sum(vd), the sum of distances to the vertices of a square, vary from different points, (x,y), inside the square? Say the square is created inside a circle of radius = 500 units and centered on (x,y) = (0,0). When the point is at (0,0), the center of the square, sum(vd) is obviously 2000, because the four vertices all fall on the perimeter of the circle at 500 units from the center and 4 * 500 = 2000:
0
sum(vd) = 2000 = sum of distances to vertices from (0,0)
When is sum(vd) at a maximum? When the point is on one or another of the vertices, which are at (+/-354,+/-354) units in relation to the center at (0,0):
sum(vd) = 2414 = sum of distances to vertices from (354,-354)
More precisely, the sum is 2414.213562373… = 1000 * (√2 + 1) units and the vertices are at (+/-353.55339…, +/-353.55339…) units, as simple geometry dictates for a square inside a circle of radius 500. Accordingly, sum(vd) varies between exactly 2000 and 2414.213562373… as the point moves inside the square:
sum(vd) = 2165 from (132,256)
sum(vd) = 2182 from (-135,271)
sum(vd) = 2069 from (177,51)
I wondered what shapes appeared as one traced the route of a point jumping, say, 1/2 towards the vertices according to tests on sum(vd). For example, if the point starts at (0,0) at time t0) and sum(vd) at time ti has to be alternately greater and less than sum(vd) at ti-1 for successive jumps, you get this shape:
jump = 1/2, test = sum(vd,ti) >,< sum(vd,ti-1)
You can use the binary number 10bin to represent the test on sum(vd) at ti-1 and ti-1, i.e. the test at jump 1 is sum(vd,ti) > sum(vd,ti-1), at step 2 is sum(vd,ti) < sum(vd,ti-1), and so on. Using the same test and a jump of 1/3, you get this shape:
jump = 1/3, test = sum(vd,ti,10bin)
Now the shape is clearly a fractal. So are some of the other shapes I found by applying the same kind of tests to a point jumping inside a pentagon:
vertex = 5, jump = 55/144 = fib(10) / fib(12), test on sum(vd) = 10bin
v = 5, j = 55/144, test = 10010bin
v = 5, j = 55/144, test = 11000bin
When test = 10010bin, you read the binary number left-to-right and check for s1><s0,s2<s1,s3<s2,s4>s3,s5<s4. Then you apply the same tests to subsequent jumps, i.e., you return to the beginning of the binary number and read it left-to-right again. Now let’s apply similar tests to hexagons and create some hex-crystals:
v = 6, j = 1/2, test = 10bin
Various hex-crystals (animated gif courtesy EZgif)
I searched an array to calculate the possible routes, so the same test yielded different results depending on dp, the depth of the search. This is because tl, the length of the test, fits more or less well into dp by dp modulo tl, that is, by whether tl is a factor of dp. For example, when the test is 110 and tl = 3, you get this with dp = 9:
v = 6, j = 1/2, test = 110, dp = 9
And you get this when dp = 10 (i.e., dp = 9+1):
v = 6, j = 1/2, test = 110bin, dp = 10dec
Here are some more hex-crystals:
test = 1100bin
test = 1110bin
test = 10010bin
test = 11010bin
test = 11100bin
test = 101000, dp = 12
test = 101100bin
test = 111100bin
test = 111100, dp = 11
test = 1110010bin
test = 1111100bin
test = 10010110bin
test = 10011110bin
test = 11000110bin
test = 11001110bin
test = 11010110bin
test = 11100110bin
test = 11101000bin
test = 11110010bin
test = 100101000bin
test = 100111110bin
test = 110011110bin
test = 110111000bin
test = 1001101010bin
test = 1001111000bin
test = 1001111010bin
test = 1010011110bin
test = 1011101110bin
test = 1101010000bin
test = 1110001110bin
test = 1110101000bin
test = 1110101010bin
test = 1111100010bin
j = 1/3, test = 1 (i.e., for all jumps sum(vd) at ti > sum(vd) at ti-1, center point
j = 2/3, test = 11100bin
j = 2/5, test = 10010bin
Finally, here are some hex-crystals based on a test of sorted distances from (x,y), i.e. how the vertices rank by distance from (x,y):
Airwolf climbing steeply (see analysis here)
3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, 1, 2, 1, 1, 12, 1, 1, 1, 3, 1, 1, 8, 1, 1, 2, 1, 6, 1, 1, 5, 2, 2, 3, 1, 2, 4, 4, 16, 1, 161, 45, 1, 22, 1, 2, 2, 1, 4, 1, 2, 24, 1, 2, 1, 3, 1, 2, 1, …
The first 5821569425 terms were computed by Eric W. Weisstein on Sep 18 2011.
The first 10672905501 terms were computed by Eric W. Weisstein on Jul 17 2013.
The first 15000000000 terms were computed by Eric W. Weisstein on Jul 27 2013.
The first 30113021586 terms were computed by Syed Fahad on Apr 27 2021.
The first 653520000000 terms were computed by Max Frank, Nov 01 2025.
• A001203 Simple continued fraction expansion of Pi.
The phosphorescent fungus Panellus stipticus, responsible for white rot (Wikipedia)
Post-Performative Post-Scriptum…
The title of this incendiary intervention is of course a core referencing of Sunn O)))’s classic album Insect Villain Monocrypt (2006).
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings. When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. All you assert is, that reason insists on the admission that, if any entities whatever have any relations which satisfy such-and-such purely abstract conditions, then they must have other relations which satisfy other purely abstract conditions.
• Alfred North Whitehead, Science and the Modern World (1925), chapter II, “Mathematics as an Element in the History of Thought”
If you go back far enough, we’re all worms. All us animals, that is. But in a subtler sense, all life is vermiform — animals, plants, fungi, bacteria. DNA is a kind of worm, a string of chemicals encoding the recipe for an animal, plant, fungus or bacterium. And the worms of DNA can be turned into numbers, just as some numbers can be turned into worms:
3/7 = 0·0.428571428571428571428571…
154/183 = 0.841530054644808743169398907…
√2 = 1.414213562373095048801688…
π = 3.1415926535897932384626433…
Those are decimals, but there’s another kind of worm for such numbers. It’s called a continued fraction:
contfrac(3/7) = [0,2,3]
contfrac(154/183) = [0,1,5,3,4,2]
contfrac(√2) = [1,2,2,2,2,2…]
contfrac(π) = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15…]
Extracting and enacting continued fractions is very simple. Here’s the extracting:
3/7 → 1/(3/7) = 7/3 = 2+1/3 – 2 = 1/3 → 1(1/3) = 3, ∴ contfrac(3/7) = [0,2,3]
154/183 → 1/(154/183) = 183/154 = 1 + 29/154 – 1 = 29/154 → 1/(29/154) = 154/29 = 5 + 9/29 – 5 = 9/29 → 1/(9/29) = 29/9 = 3 + 2/9 – 3 = 2/9 → 1/(2/9) = 9/2 = 4 + 1/2 – 4 = 1/2 → 1/(1/2) = 2 – 2 = 0, ∴ contfrac(154/183) = [0,1,5,3,4,2]
And here’s the enacting:
[0,2,3] → 3 → 1/3 → 1/3 + 2 = 7/3 → 1/(7/3) = 3/7
[0,1,5,3,4,2] → 2 → 1/2 → 1/2 + 4 = 9/2 → 2/9 + 3 = 29/9 → 9/29 + 5 = 154/29 → 29/154 + 1 = 183/154 → 1/(183/154) = 154/183
Once you’ve got the worm of a continued fraction, you can perm the worm, as it were, generating different fractions like this (I’m dropping the initial [0,…] of the contfracs):
[2,3,4] = contfrac(13/30)
[2,4,3] → 13/29
[3,2,4] → 09/31
[3,4,2] → 09/29
[4,2,3] → 07/31
[4,3,2] → 07/30
Reversing a continued fraction is a kind of permutation, so the fractal below represents one kind of worms in terms of perms:
Variant of a limestone fractal or gryke fractal
I call that graph a fract-L, because it’s shaped like an L and the x axis represents the simplified fractions 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5…, while the y axis represents the fractions you get by reversing the continued fractions of 1/2, 1/3, 2/3…:
contfrac(1/2) = [2] → 1/2
contfrac(1/3) = [3] → 1/3
contfrac(2/3) = [1,2] → 1/3
contfrac(1/4) = [4] → 1/4
contfrac(3/4) = [1,3] → 1/4
contfrac(1/5) = [5] → 1/5
contfrac(2/5) = [2,2] → 2/5
contfrac(3/5) = [1,1,2] → 2/5
contfrac(4/5) = [1,4] → 1/5
contfrac(1/6) = [6] → 1/6
contfrac(5/6) = [1,5] → 1/6
contfrac(1/7) = [7] → 1/7
contfrac(2/7) = [3,2] → 3/7
contfrac(3/7) = [2,3] → 2/7
contfrac(4/7) = [1,1,3] → 2/7
contfrac(5/7) = [1,2,2] → 3/7
contfrac(6/7) = [1,6] → 1/7
contfrac(1/8) = [8] → 1/8
contfrac(3/8) = [2,1,2] → 3/8
contfrac(5/8) = [1,1,1,2] → 3/8
contfrac(7/8) = [1,7] → 1/8
contfrac(1/9) = [9] → 1/9
contfrac(2/9) = [4,2] → 4/9
contfrac(4/9) = [2,4] → 2/9
contfrac(5/9) = [1,1,4] → 2/9
contfrac(7/9) = [1,3,2] → 4/9
contfrac(8/9) = [1,8] → 1/9
[…]
If you perm the worm in other ways, you get other shapes on the fract-L. I looked at continued fractions of fixed length, 4, 5 and 6, and permed them using one of the permutations of [1,2,3,4], [1,2,3,4,5] and [1,2,3,4,5,6]. Here’s a graph for fractions, a/b, and permed fractions, perm(a/b), where length(contfrac(a/b)) = 4:
x = a/b when length(contfrac(a/b)) = 4, y = fraction from contfrac(a/b) permed with [1,3,2,4]
The x axis represents simplified fractions, a/b, when len(cf(a/b)) = 4. The y axis represents the fractions found by applying the perm [1,3,2,4] to contfrac(a/b). That is, the first number of the contfrac stays where it is, the third number moves to position 2, the second number moves to position 3 and the fourth number stays where it is. In short, you simply swap the middle two numbers of contfrac(a/b). Here’s an example:
contfrac(9/43) = [4,1,3,2] → [4,3,1,2] → 11/47, because contfrac(11/47) = [4,3,1,2]
Here are more fract-Ls representing worms in terms of perms:
fract-L for contfrac(a/b) permed by [2,1,3,4]
fract-L for contfrac(a/b) permed by [3,2,1,4]
fract-L for contfrac(a/b) permed by [1,4,2,3,5] (i.e. a/b where len(contfrac(a/b)) = 5)
fract-L for contfrac(a/b) permed by [1,5,3,4,2]
fract-L for contfrac(a/b) permed by [2,1,4,3,5]
fract-L for contfrac(a/b) permed by [3,4,1,2,5]
fract-L for contfrac(a/b) permed by [4,2,3,1,5]
fract-L for contfrac(a/b) permed by [4,2,5,3,1]
fract-L for contfrac(a/b) permed by [4,3,2,1,5]
fract-L for contfrac(a/b) permed by [5,3,4,2,1]
fract-L for contfrac(a/b) permed by [2,1,4,3,5,6] (i.e. a/b where len(contfrac(a/b)) = 6)
fract-L for contfrac(a/b) permed by [2,1,5,4,3,6]
fract-L for contfrac(a/b) permed by [3,2,1,4,5,6]
fract-L for contfrac(a/b) permed by [3,2,1,5,4,6]
fract-L for contfrac(a/b) permed by [3,5,1,4,2,6]
fract-L for contfrac(a/b) permed by [4,2,5,1,3,6]
fract-L for contfrac(a/b) permed by [4,3,2,1,5,6]
fract-L for contfrac(a/b) permed by [4,5,2,3,1,6]
fract-L for contfrac(a/b) permed by [1,3,2,6,5,4,7] (i.e. a/b where len(contfrac(a/b)) = 7)
fract-L for contfrac(a/b) permed by [1,5,2,6,3,4,7]
fract-L for contfrac(a/b) permed by [5,6,3,7,4,1,2]
fract-L for contfrac(a/b) permed by [6,2,3,5,4,1,7]
fract-L for contfrac(a/b) permed by [6,2,5,4,7,3,1]
Post-Performative Post-Scriptum
Much as I hate the phrase “in terms of”, I was happy to use it in the title of this post. After all, it isn’t ugly but assonant there. And it began life in mathematics, where it still has its proper meaning rather than being pretentious and prolix:
How did this complex preposition come into being? The OED [Oxford English Dictionary] reveals that it has been in use since the mid-18c. as a mathematical expression “said of a series…stated in terms involving some particular (my emphasis) quantity”, and illustrates this technical usage by citing examples from the work of Herbert Spencer (1862), J. F. W. Herschel (1866), and other writers. From this technical use came at first a trickle and, after the 1940s, a flood of imitative uses by non-mathematicians. — “Terminal Trinity”
Elsewhere Other-Engageable
• A Fracteasel on a Fract-L — an earlier look at continued fractions and fractal fract-Ls
The Fibonacci sequence is beautiful like clockwork. There’s a perfectly clear, rigorously defined mechanism ticking out an entirely predictable result for ever:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, … — A000045 at the Online Encyclopedia of Integer Sequences (OEIS)
And there’s a formula to calculate any term in the sequence without calculating all the terms that precede it:
Binet’s formula for Fn, the n-th Fibonacci number
But I also like sequences that you might call definitely arbitrary. That is, there’s a perfectly clear, rigorously defined mechanism, but the results seem arbitrary — not predictable at all:
6, 15, 5, 22, 6, 3, 30, 9, 7, 2, 45, 15, 6, 5, 1, 36, 14, 6, 5, 3, 1, 62, 22, 16, 6, 5, 3, 2, 69, 21, 15, 4, 9, 5, 2, 1, 84, 30, 15, 9, 6, 7, 2, 2, 1, 56, 22, 13, 7, 3, 5, 2, 0, 0, 0, 142, 45, 22, 15, 12, 6, 9, 5, 3, 1, 2, 53, 17, 8, 4, 5, 1, 6, 3, 1, 1, 1, 0, 124, 36, 27, 14, 18, 6, 6, 5, 2, 3, 1, 1, 0, … A349083 at OEIS
What’s the formula there? That sequence is defined at the OEIS as “The number of three-term Egyptian fractions of rational numbers x/y, 0 < x/y < 1, ordered as below. The sequence is the number of (p,q,r) such that x/y = 1/p + 1/q + 1/r where p, q, and r are integers with p < q < r.” For example: “The sixth rational number is 3/4 [and] 3/4 = 1/2 + 1/5 + 1/20 = 1/2 + 1/6 + 1/12 = 1/3 + 1/4 + 1/5, so a(6)=3.”
Feathers by Ben Rothery (click for larger)
Post-Performative Post-Scriptum
“Bennae Bellae” is a play on Pennae Bellae, which is Latin for “Beautiful Feathers” (Pennae Pulchrae would be better, but not as assonant).
I wondered what happened when you take a fraction, a/b, and calculate a/b – (a/b)^2 = c/d. And an interesting pattern appeared when I tried a prime denominator and all numerators less than that denominator. Here’s the pattern with the prime denominator of 7:
1/7 - 01/49 = 06/49
2/7 - 04/49 = 10/49
3/7 - 09/49 = 12/49
4/7 - 16/49 = 12/49
5/7 - 25/49 = 10/49
6/7 - 36/49 = 06/49
And here it is with the prime denominator of 13:
01/13 - 001/169 = 12/169
02/13 - 004/169 = 22/169
03/13 - 009/169 = 30/169
04/13 - 016/169 = 36/169
05/13 - 025/169 = 40/169
06/13 - 036/169 = 42/169
07/13 - 049/169 = 42/169
08/13 - 064/169 = 40/169
09/13 - 081/169 = 36/169
10/13 - 100/169 = 30/169
11/13 - 121/169 = 22/169
12/13 - 144/169 = 12/169
It’s easier to see what’s going on with the smaller denominator:
1/7 - 01/49 = 06/49 = 1/7 - (1/7)^2
2/7 - 04/49 = 10/49 = 2/7 - (2/7)^2
3/7 - 09/49 = 12/49 = 3/7 - (3/7)^2
4/7 - 16/49 = 12/49
5/7 - 25/49 = 10/49
6/7 - 36/49 = 06/49
1/7 - 01/49 = 07/49 - 01/49 = 06/49
2/7 - 04/49 = 14/49 - 04/49 = 10/49
3/7 - 09/49 = 21/49 - 09/49 = 12/49
4/7 - 16/49 = 28/49 - 16/49 = 12/49
5/7 - 25/49 = 35/49 - 25/49 = 10/49
6/7 - 36/49 = 42/49 - 36/49 = 06/49
1/7 - 01/49 = 1*7/7^2 - 1^2/7^2 = 07/49 - 01/49 = 06/49
2/7 - 04/49 = 2*7/7^2 - 2^2/7^2 = 14/49 - 04/49 = 10/49
3/7 - 09/49 = 3*7/7^2 - 3^2/7^2 = 21/49 - 09/49 = 12/49
4/7 - 16/49 = 4*7/7^2 - 4^2/7^2 = 28/49 - 16/49 = 12/49
5/7 - 25/49 = 5*7/7^2 - 5^2/7^2 = 35/49 - 25/49 = 10/49
6/7 - 36/49 = 6*7/7^2 - 6^2/7^2 = 42/49 - 36/49 = 06/49
Here’s a set of the patterns using prime denominators from 3 to 13:
1/3 - 1/9 = 2/9
2/3 - 4/9 = 2/9
1/5 - 01/25 = 4/25
2/5 - 04/25 = 6/25
3/5 - 09/25 = 6/25
4/5 - 16/25 = 4/25
1/7 - 01/49 = 06/49
2/7 - 04/49 = 10/49
3/7 - 09/49 = 12/49
4/7 - 16/49 = 12/49
5/7 - 25/49 = 10/49
6/7 - 36/49 = 06/49
01/11 - 001/121 = 10/121
02/11 - 004/121 = 18/121
03/11 - 009/121 = 24/121
04/11 - 016/121 = 28/121
05/11 - 025/121 = 30/121
06/11 - 036/121 = 30/121
07/11 - 049/121 = 28/121
08/11 - 064/121 = 24/121
09/11 - 081/121 = 18/121
10/11 - 100/121 = 10/121
01/13 - 001/169 = 12/169
02/13 - 004/169 = 22/169
03/13 - 009/169 = 30/169
04/13 - 016/169 = 36/169
05/13 - 025/169 = 40/169
06/13 - 036/169 = 42/169
07/13 - 049/169 = 42/169
08/13 - 064/169 = 40/169
09/13 - 081/169 = 36/169
10/13 - 100/169 = 30/169
11/13 - 121/169 = 22/169
12/13 - 144/169 = 12/169
Then I tried a/b – (a/b)^3. There were no obvious strong patterns, but something caught my eye in the last subtraction for b = 19:
01/19 - 0001/6859 = 0360/6859 = 1/19 - (1/19)^3
02/19 - 0008/6859 = 0714/6859 = 2/19 - (2/19)^3
03/19 - 0027/6859 = 1056/6859 = 3/19 - (3/19)^3
04/19 - 0064/6859 = 1380/6859
05/19 - 0125/6859 = 1680/6859
06/19 - 0216/6859 = 1950/6859
07/19 - 0343/6859 = 2184/6859
08/19 - 0512/6859 = 2376/6859
09/19 - 0729/6859 = 2520/6859
10/19 - 1000/6859 = 2610/6859
11/19 - 1331/6859 = 2640/6859
12/19 - 1728/6859 = 2604/6859
13/19 - 2197/6859 = 2496/6859
14/19 - 2744/6859 = 2310/6859
15/19 - 3375/6859 = 2040/6859
16/19 - 4096/6859 = 1680/6859
17/19 - 4913/6859 = 1224/6859
18/19 - 5832/6859 = 0666/6859
Look at the final subtraction: 18/19 – 5832/6859 = 666/6859. So the Number of the Beast is the numerator when 18/19 is decreased by (18/19)^3. Dropping the need for powers of a/b, I looked for more beastly fraction subtractions using pairs of simplified fractions. Here are a few:
26/35 - 04/31 = 666/1085 = 0.613824885...
29/35 - 05/29 = 666/1015 = 0.656157635...
32/35 - 02/23 = 666/0805 = 0.827329193...
40/41 - 14/31 = 666/1271 = 0.523996853...
35/43 - 13/35 = 666/1505 = 0.442524917...
23/47 - 01/31 = 666/1457 = 0.457103638...
30/47 - 12/41 = 666/1927 = 0.345614946...
31/47 - 01/23 = 666/1081 = 0.616096207...
31/47 - 02/46 = 666/1081 = 0.616096207...
40/47 - 02/19 = 666/0893 = 0.745800672...
[...]
This fraction subtraction is beastly in two ways: 95/103 – 83/97 = 666/9991 = 0.066659994…
I also noticed that 666 can be the numerator in two ways when the denominator is 19 and its powers:
18/19 - 5832/6859 = 666/6859 = 18/19 - (18/19)^3
18/19 + 0324/0361 = 666/0361 = 18/19 + (18/19)^2
So 666 is both the Number of the Decreased and the Number of the Increased. That double pattern is general when you either decrease (b-1)/b by ((b-1)/b)^3 or increase (b-1)/b by ((b-1)/b)^2:
2/3 - 8/27 = 10/27 = 2/3 - (2/3)^3
2/3 + 04/9 = 10/09 = 2/3 + (2/3)^2
4/5 - 64/125 = 36/125 = 4/5 - (4/5)^3
4/5 + 16/025 = 36/025 = 4/5 + (4/5)^2
6/7 - 216/343 = 78/343 = 6/7 - (6/7)^2
6/7 + 036/049 = 78/049 = 6/7 + (6/7)^2
10/11 - 1000/1331 = 210/1331
10/11 + 0100/0121 = 210/0121
12/13 - 1728/2197 = 300/2197
12/13 + 0144/0169 = 300/0169
16/17 - 4096/4913 = 528/4913
16/17 + 0256/0289 = 528/0289
18/19 - 5832/6859 = 666/6859
18/19 + 0324/0361 = 666/0361
22/23 - 10648/12167 = 990/12167
22/23 + 00484/00529 = 990/00529
Overlord In Terms of Core Issues Around Maximal Engagement with Key Notions of the Über-Feral 
