Der Pharao des Farnen

Clark Ashton Smith and some ferns in 1958 (Eldritch Dark)

I, too, am capable of observation; but I am far happier when I create everything in a story, including the milieu. This is why I do my best in work like “Satrampa Zeiros”. Maybe I haven’t enough love for, or interest in, real places to invest them with the atmosphere that I achieve in something purely imaginary. […] As for the problem of phantasy, my own standpoint is that there is absolutely no justification for literature unless it serves to release the imagination from the bounds of everyday life. I have undergone a complete revulsion against the purely realistic school, including the French, and can no longer stomach even Anatole France. […] Well, I must put a scientific — or at least a pseudo-scientific — curb on my fancy if I am to sell anything. — Clark Ashton Smith, letter to H.P. Lovecraft, 9th January 1930


The Wine of Words: Valorizing the Verbiviniculture of Clark Ashton Smith

Mathemorchids

Flowers are modified leaves. That’s a scientific fact. And it must depend on the way the genetic program of a plant allows for change in variables of growth — in the relative dimensions, directions and forms of various collections of cells.

But I wasn’t thinking of flowers or leaves or botany when I wrote a program to trace the path taken by a point moving in various ways between the center and perimeter of a circle. After I’d run the program, I was definitely thinking of flowers and leaves. How could I not be, when they appeared on the screen in front of my eyes? By adjusting variables in the program, I could produce either flowers or leaves or something between the two:

Flower without color


Flower with color






Some of the flower-shapes reminded me of orchids, so I called them mathemorchids. The variables I used governed this procedure:

defprocmathemorchid
rd = 0
jump = jmin
jinc = +1
repeat
xr = xc + int(sin(rd) * rdius + sin(rd * xmult) * xminl)
yr = yc + int(cos(rd) * rdius + cos(rd * ymult) * yminl)
jump = jump + jinc
if(jump = jmin) or (jump >= jmax) then jinc = -jinc
procDrawLine(xr,yr,xc,yc,jump)
rd = rd + rdinc
until rd > maxrd
endproc

Here are explanations of the variables:

rd — short for radian and setting the angle of the point, 0 to maxrd = pi * 2, as it moves between the center and perimeter of the circle
rdinc — the amount by which rd is incremented
xc, yc — the center of the circle
rdius — the radius of the circle
xr, yr — the adjustable radiuses used in trigonometric calculations for the x and y dimensions
xmult, ymult — used to multiply rd for further trig-calcs using…
xminl, yminl — the lengths by which xr and yr are adjusted
jmin, jmax — these are the lower and upper bounds for a rising and falling variable called jump, which determines how far the point moves before it’s marked on the screen

If you look at the use of the sine and cosine functions, you’ll see that the point can swing back on its path or swing ahead of itself, as it were. That’s how the path of the point can simulate three-dimensionality as it lays down thicker or thinner patches of pixels.

Here are the mathemorchids, leaves, scallops and other shapes created by adjusting the variables described above (with more of the generating program as an appendix):

Mathemorchid for jmin = 6, jmax = 69, xmult = 7, ymult = 7, xminl = 40, yminl = 88 (see file-name)





























 

















And here are a few more examples of the mathemorchids and other shapes look like without color:





 



Code for creating the Mathemorchids

defprocmathemorchid
rd = 0
rd = 0
jump = jmin
jinc = +1
repeat
xr = xc + int(sin(rd) * rdius + sin(rd * xmult) * xminl)
yr = yc + int(cos(rd) * rdius + cos(rd * ymult) * yminl)
jump = jump + jinc
if(jump = jmin) or (jump >= jmax) then jinc = -jinc
procDrawLine(xr,yr,xc,yc,jump)
rd = rd + rdinc
k=inkey(0)
until rd > maxrd or k > -1
endproc

defprocDrawLine(x1,y1,x2,y2,puttest)
xdiff = x1 – x2
ydiff = y1 – y2
if abs(xdiff) > abs(ydiff) then
yinc = -ydiff / abs(xdiff)
if xdiff < 0 then xinc = +1 else xinc = -1
else
xinc = -xdiff / abs(ydiff)
if ydiff colrmx then col = 1
put = 0
endif
if int(x) x2 then x = x + xinc
if int(y) y2 then y = y + yinc
iffunc=2then
ifx<x_lo x_lo=x
ifyx_hi x_hi=x
ify>y_hi y_hi=y
endif
until fnreached
endproc

deffnreached
if xinc > 0 then
xreached = int(x) >= x2
else
xreached = int(x) 0 then
yreached = int(y) >= y2
else
yreached = int(y) <= y2
endif
= xreached and yreached
end

Ho Rhodornix

Y Rhosyn a’r Wylan

There’s a rose at Number Seven,
Tho’ the air is wintered now,
And it glows at Number Seven,
In the brain behind thy brow.

There’s a gull that turns the stillness
Of the air above thy head:
’Tis the gull that spurns the illness
Of the creed where color’s dead.

There’s a rose at Number Seven;
There’s a gull that turns the air:
And what glows at Number Seven
Is the spurner turning there.

Green Grass Growing

green (adj.)

Old English grene, Northumbrian groene “green, of the color of living plants,” in reference to plants, “growing, living, vigorous,” also figurative, of a plant, “freshly cut,” of wood, “unseasoned” earlier groeni, from Proto-Germanic *grōni- (source also of Old Saxon grani, Old Frisian grene, Old Norse grænn, Danish grøn, Dutch groen, Old High German gruoni, German grün), from PIE root *ghre- “grow” (see grass), through sense of “color of growing plants.”


grass (n.)

Old English græs, gærs “herb, plant, grass,” from Proto-Germanic *grasan, which, according to Watkins, is from PIE *ghros- “young shoot, sprout,” from root *ghre- “to grow, become green,” thus related to grow and green, but not to Latin grāmen “grass, plant, herb.”


grow (v.)

Middle English grouen, from Old English growan (of plants) “to flourish, increase, develop, get bigger” (class VII strong verb; past tense greow, past participle growen), from Proto-Germanic *gro-, from PIE root *ghre- “to grow, become green” (see grass).


EtymOnline

Future Floral Font

Odoric (also known as Odoryc, Odorous, Dendric, Dryadic, Floric, and Floral) will be a language of odors used by many races of intelligent tree and a few races of intelligent flower for an indefinite period between 15,000,000 and 20,000,000 years in the future. In its standard form among trees it will be based on odors released from special odorifera (scent-organs) on leaves or branches and wafted from tree to tree by the wind or air-diffusion. Because of the chemical nature of Odoric, a simple exchange of greetings will take several hours in favorable weather, a brief conversation several days, and the recitation of an average tree-saga a year or more.

Odoric will have innumerable and often mutually unintelligible dialects falling into three main families: Coniferous Odoric, as used by conifers; Deciduous Odoric, as used by non-coniferous deciduous trees; and Floral Odoric, as used by flowers. Its native written form will evolve late and be based on chemical markers laid down within leaves and roots as a mnemonic for individual trees. In this form, it cannot be represented directly by a script suitable for human eyes, but Odoric will also be written by a non-plant species: an advanced race of intelligent squirrel that will discover and transcribe the language about 28,000,000 years in the future. This Sciurine (Squirrel) Odoric is presented here in one of its several forms.

As can be seen, the letters, or osmemes, of the script fall into six eight-letter scent-series named after the closest equivalent scent in the present-day plant kingdom. The letters of each series will be distinguished in their wafted (that is, “spoken”) form by subtle chemical variations, although some may be created artificially to complete an incomplete series – eight will apparently have mystical significance for squirrels, perhaps under the influence of a mathematic mysticism among trees. For example, seems to be a homosme of , or to become so in some dialects of Odoric. Each letter is transcribed into Roman using the initial of the scent in the series to which it will belong, plus a subscripted digit indicating its place in the series: the second letter of the Jasmine series, , is therefore J2 and the fifth letter of the Honeysuckle series, , is H5.

There will be only two punctuation marks in this form of Sciurine Odoric: <  >, used like a comma, semi-colon, or colon, and <  >, used like a full stop. It is believed that these marks will have no wafted form and will be used purely for the convenience of the squirrels transcribing a passage of Odoric.

Sample text

Transliteration
L3H1C5L6C6 J6H4J8C2C5S1 L2H7L7C6V8V5 L7C2S6C4L2H7 C6H8J5H3C6J6H4 L7C2S6C4L2H7L7C6 L3H1C5L6C6V2, H3C6J6H4J8C2 H4J8C2C5S1J1V5J4 L2H7L7C6V8V5 L7C2S6C4L2H7 L7C2S6C4L2H7L7C6 L2H7L7C6V8V5 C2L3H1C5L6C6V2V7 L7C2S6C4L2H7L7C6 L3H1C5L6C6V2, H7L7C6V8V5C5 L7C2S6C4L2H7 L7C2S6C4L2H7L7C6 L2L7C2H8C6V7S6 L2L7C2H8C6 L7C2S6C4L2H7L7C6 L3H1C5L6C6V2, S1J1V5J4L7C2 L7C2S6C4L2H7 L7C2S6C4L2H7L7C6 C6V8V5C5C2L3H1C5 L3L2L7C2H8 C2S6C4L2H7 L7C2H8C6 L7C2S6C4L2H7L7C6 L3H1C5L6C6V2 C5C2L3H1C5L6 L7C2S6C4L2H7 C2L3H1C5L6C6V2 J4L7C2S6C4L2H7L7. C5S1J1V5J4 L3H1C5L6C6 L7C2S6C4L2H7 C2C5S1J1V5J4L7C2 L3H1C5L6C6V2, J6H4J8C2C5S1 L7C2S6C4L2H7 C2C5S1J1V5J4L7 L3H1C5L6C6V2, L2H7L7C6V8V5 H3C6J6H4J8C2 L7C2S6C4L2H7 L7C2S6C4L2H7L7C6 J1V5J4L7C2S6 L3H1C5L6C6V2, L2L7C2H8C6V7S6 H7L7C6V8V5C5 L7C2S6C4L2H7 L7C2S6C4L2H7L7C6 J8C2C5S1J1V5J4 L3H1C5L6C6V2, C5C2L3H1C5L6 L7C2S6C4L2H7L7C6 S1J1V5J4L7C2 L7C2S6C4L2H7 L7C2S6C4L2H7L7C6 L2L7C2H8C6V7 L2L7C2H8C6 L7C2S6C4L2H7L7C6 L3H1C5L6C6V2 L7C2H8C6V7S6L6 L7C2S6C4L2H7 C2L3H1C5L6C6V2 J4L7C2S6C4L2H7L7.

Literal translation
sun rain with thou bless plural subj, leaf branch with thou plural wind stifle plural subj, root thou plural earth eat plural subj, seed thou plural number adj not be plural subj true thou stand future. but sun thou scorch subj, rain thou drown subj, wind leaf thou plural tear subj, earth root thou plural crush subj, worm plural seed thou plural each eat plural subj false thou stand future.

Idiomatic translation

“May the sun and rain bless thee, thy leaves and branches stifle the wind, thy roots swallow the (whole) earth, thy seeds be innumerable if thou art true. But may the sun scorch thee, the rain drown thee, the wind tear thy leaves, the earth crush thy roots, worms eat all thy seeds if thou art false.” – Traditional Odoric formula used to seal vows and treaties.

© 2005 Simon Whitechapel

Vers d’un Veuf

El Desdichado

Je suis le Ténébreux, – le Veuf, – l’Inconsolé,
Le prince d’Aquitaine à la tour abolie :
Ma seule étoile est morte, – et mon luth constellé
Porte le Soleil noir de la Mélancolie.

Dans la nuit du tombeau, toi qui m’as consolé,
Rends-moi le Pausilippe et la mer d’Italie,
La fleur qui plaisait tant à mon cœur désolé,
Et la treille où le pampre à la rose s’allie.

Suis-je Amour ou Phébus ?… Lusignan ou Biron ?
Mon front est rouge encor du baiser de la reine ;
J’ai rêvé dans la grotte où nage la syrène…

Et j’ai deux fois vainqueur traversé l’Achéron :
Modulant tour à tour sur la lyre d’Orphée
Les soupirs de la sainte et les cris de la fée.

Gérard de Nerval, Les Chimères (1856)


The Misfortunate One

I am the Dark One, – the Widower, – the Inconsolable,
The Prince of Aquitaine in the ruined tower:
My only star is dead, – and my star-studded lute
Bears the black Sun of Melancholy.

In the night of the tomb, thou who consoledst me,
Give me back Posillipo and the Italian sea,
The flower that so pleased my desolate heart,
And the vine where the tendril entwines with the rose.

Am I Love or Phoebus?… Lusignan or Biron?
My brow is still red from the queen’s kiss;

I dreamed in the grotto where the siren swims…

And twice victorious I crossed the Acheron:
Fingering in turn from Orpheus’s lyre
The sighs of the saint and the cries of the fairy.

The Wyrm Ferns

A fern is a fractal, a shape that contains copies of itself at smaller and smaller scales. That is, part of a fern looks like the fern as a whole:

Fern as fractal (source)


Millions of years after Mother Nature, man got in on the fract, as it were:

The Sierpiński triangle, a 2d fractal


The Sierpiński triangle is a fractal created in two dimensions by a point jumping halfway towards one or another of the three vertices of a triangle. And here is a fractal created in one dimension by a point jumping halfway towards one or another of the two ends of a line:

A 1d fractal


In one dimension, the fractality of the fractal isn’t obvious. But you can try draggin’ out (or dragon out) the fractality of the fractal by ferning the wyrm, as it were. Suppose that after the point jumps halfway towards one or another of the two points, it’s rotated by some angle around the midpoint of the two original points. When you do that, the fractal becomes more and more obvious. In fact, it becomes what’s called a dragon curve (in Old English, “dragon” was wyrm or worm):

Fractal with angle = 5°


Fractal 10°


Fractal 15°


Fractal 20°


Fractal 25°


Fractal 30°


Fractal 35°


Fractal 40°


Fractal 45°


Fractal 50°


Fractal 55°


Fractal 60°


Fractal 0° to 60° (animated at ezGif)


But as the angle gets bigger, an interesting aesthetic question arises. When is the ferned wyrm, the dragon curve, at its most attractive? I’d say it’s when angle ≈ 55°:

Fractal 50°


Fractal 51°


Fractal 52°


Fractal 53°


Fractal 54°


Fractal 55°


Fractal 56°


Fractal 57°


Fractal 58°


Fractal 59°


Fractal 60°


Fractal 50° to 60° (animated)


At angle >= 57°, I think the dragon curve starts to look like some species of bristleworm, which are interesting but unattractive marine worms:

A bristleworm, Nereis virens (see polychaete at Wikipedia)


Finally, here’s what the ferned wyrm looks like in black-and-white and when it’s rotating:

Fractal 0° to 60° (b&w, animated)


Fractal 56° (rotating)


Fractal 56° (b&w, rotating)


Double fractal 56° (b&w, rotating)


Previously Pre-Posted (Please Peruse)…

Curvous Energy — a first look at dragon curves
Back to Drac’ — another look at dragon curves

Toxic Turntable #30

Currently listening…

• Vrocsec, Rosa sub Luna (1981)
• Usward Quenched, Trust the Dust (2006)
• Under the Willows, Of Mouse and Man (1999)
• Doom Quota, A Gloomier Land Never Was (2009)
• Jay Victor Caldwell, Symphony in V Minor (1926)
• Elementic TS, Eight’s Too Late (2022)
• Gauntlet Fox, Evensongs of Eleven Counties (1971)
• Les Xenonymphes, Acétone (1995)
• Gnosthrill, God Gnose (1998)
• Malodious, Τῶν Βδελυγμάτων τῆς Γῆς (2007)
• Yickthraite, Om Gom Nom (1997)
• Koukog, Gluehouse (1997)
• Harold Meistmeyer, Best Of (1986)
• Uzuzuzu, We Want Wonders (1992)
• Kotzu, Zone of Clones (1985)
• Liam Tolloway, Ragtime Rex (1913)
• Ptosis, 1991 (1992)
• Nsurosus, Eight Cold Moons (1975)
• Rita Haunts Rita, Ghost to Ghost (2017)


Previously pre-posted:

Toxic Turntable #1#2#3#4#5#6#7#8#9#10#11#12#13#14#15#16#17#18#19#20#21#22#23#24#25#26#27#28#29