From The Archive #3: Fractal Poetry by Michael G. Smith

Fractals in Nature and Mathematics

One way we see, model and construct/deconstruct the world is by the use of traditional (Euclidean) shapes of geometry, i.e. circles, squares, pyramids, spheres. For example, we can design and build a house (or deconstruct one) using such regular shapes. However, how would an irregular- or fragmented- shaped object, such as a mountain chain, coastline, tree, a snowflake, the Grand Canyon, a sprig of broccoli be modeled or constructed? If one looks closely at such objects, they might see that they can be broken apart into a shape that is a “reduced copy of the whole”. For example, the two-dimensional surface of mountain range can be modeled as a collection of triangles. Mathematically this is accomplished by taking a “seed” reflective of the whole, plugging it into an algorithm and continually iterating (repeating) the algorithm again and again. In this process, called recursion, the seed feedbacks on itself, further adding to and refining the resulting object.
The mathematical objects created by such iterative processes are called fractals,
a term coined by Benoît Mandelbrot in 1975. Fractals have their root in fractus, meaning broken or fractured. The dimensionality of a fractal is fractional, i.e. 1.39 or 1.67, and often between 1 and 2. Since the number of fractions is much greater than the number of whole numbers (0, 1, 2…) the number of fractals, and hence fractal dimensions and objects, dwarfs our habitual 2-D and 3-D views of the universe.
A well-known example of fractal mathematics used to model a a snowflake begins with an equilateral triangle (a triangle whose sides have the same length). The middle third of every side of the triangle is replaced with a pair of lines that form an equilateral “bump”. The result is called a Koch snowflake when iterated. A video of the process shows that only a few iterations will transform a triangle into a snowflake. I encourage you to watch the PBS Nova special ( about the history of fractal mathematics and to see how other objects are made.
To summarize, a fractal is a mathematical object that begins with a seed and grows, or as a friend of mine said, “as above, so below”. And, much like poetry and art, fractal mathematics is a geometry that finds order out of chaos.

Fractals in Art and Poetry

The recursive nature of fractal mathematics is often employed in media, animation, and digital art. Computer screensavers are one common example. Fractals are also found in “traditional” art. Computer analysis has shown fractal patterns appear in the paintings of Jackson Pollock. Why might Pollack’s paintings have fractal regions embedded in them?
Intentionally and unintentionally poets write fractal poems. A fractal poem is one that employs a seed phrase, uses symmetry and repetition of word-types and sounds, and considers dimensionality. Diana Der Hovanessian, with a nod to Edna St. Vincent Millay, beautifully describes the transition from Euclidean geometry to fractal geometry in her surprising poem Fractals (see Fractals is iteration on the traditions of mathematics and poetry!

Below are four other fractal poems that exhibit different aspects of fractals. Consider the following questions while you read the poems or say them aloud:

What is the seed, or seeds, of each poem?
What words or word-types add texture and dynamics to the poem and help move it? Consider the multiplicity of meanings that some of the words have;
How does the scale of the poem progress? Does it move outward, inward, or in another direction? What does this reveal to the reader about the author’s life or scene?
How does the author “escape” the fractal iteration and end the poem? What might this hint about the things that lie beyond the poem?

Escaping the Mandelbrot Set

Robin Chapman

She says
The coffee is fine
Though it could have been stronger
And cream would be nice.

She says
The weather today
Is, yes, fine, though cold
For summer and more rain likely tonight.

She says
The summer’s going well,
Of course awfully fast and won’t last
Long enough to get done what she’d planned.

She says
The marriage was ten good years
And then ten bad, and she’s learned
A lot since, though of course it’s lonely.

She says
Buying a new cappuccino maker,
Espresso roast, and best jam for her bread
Is frivolous, but we only have one life.

Published in Images of a Complex World: The Art and Poetry of Chaos,
Robin Chapman and Julien Clinton Sprott, World Scientific Publishing Co. Pte., Ltd., 2005, p. 116.

Daniel Stewart

If no one; if nothing, if not me; if burning; if wing; if organ

(failing); eyes: mouths. Vise.

If trap knows teeth. If nerve knows cruel. If heart knows blood. If
water tongues fire.

Hiss of water. If hand kneads fire. If instinct (:desire). If seasonal,
flower. If I the liar.

I the liar. If God’s lips glazed with pollen’s praise.

If flight is ache is palm frond’s wince in salt and wind.

If whale, fin and foam, wave and spray.

If Man-O-War, promise sting.

If Monarch, splinter chrysalis into rein.

Published in Prairie Schooner, Spring 2011.

Arthur Sze

Stopped at an intersection,
ruminating on how, in
a game of go, to consider all
the possible moves until
the end would take a computer
longer than the expected
lifetime of the universe,
you flit from piccolo
to stovepipe in a letter,
to scrutinizing faces
while standing in line
at the post office, to weather
forecast – a snowflake
has an infinite number of possible shapes –
consider, only last weekend,
a wasp threaded along a
screen door in south light,
mark the impulse to – not
see this, do that – water
leafing pear trees along
a curved driveway, relax
the intricate openwork mesh
of spring, recall lifting
a packet of flax seed
off the counter, and, checking
for an expiration date,
note – red light, green light –
sow when danger of
frost is past, then go, go.

Published in The Ginkgo Light, Copper Canyon Press, 2009, p. 55.
Purification Fractal

Michael G. Smith

Grand Canyon National Park

Booted, at the rim
step down forward

start reverse
step a minute, a day

sixty-thousand years
step, stepped, steeped

dry tawny Toroweap
my eyes weep

weeping, last night’s rain
pooled in sepia Esplanade

here is camp
tinaja, sandstone,

limestone, sandstone
salty sea bones

here is rattlesnake
here memory falls

form forming warping
worked Amerindian stone

working tool
clatter clattered

conglomerate rubble
sandstone, limestone

ocean silted
Red Wall limestone

rubbled, rubble
blistered, blistering

feet step, stepped,
layered, layers

faulted, avalanched
bloody pricks

of desert bricklebrush
proffered prickly pear

thunder thundered river
from sandstone wall

here is two-night camp
scorpion, scorpion-eating

pallid bat, hear pack rat
scurry, cottonwood rustle

silent great-horned owl,
hear morning camp-robber

raven flap flap
we hit the trail ahead

slick rain slickened
tumbled down

Cardenas ball-bearing
lava, Shinumo shale

narrow ledge
exposed exposure

above flowing
Tapeats ribbon

flowing into early,
early energy, pressured

heated folded
folded heated

folded river-severed
black, blackened, buried

two-billion-year old schist
gracing our handholds

released again
to movement

While it may seem these poems are no different than other “stream-of-consciousness” or abstract poems, there can be no doubt they affect the reader’s senses differently, such as haiku does. I, for one, get chills and tingles when I read and recite such poems. Or write one. Such results do not surprise me – the human circulatory system with its beating heart at the center, beginning and end is the quintessential fractal system found in Nature.

My First Creative Moment by Karla Linn Merrifield

My First Creative Moment
by Karla Linn Merrifield

Many, many moons ago—in 1967—my brother inspired my first poem, a short one of two stanzas that lamented our relationship: “I love him much/he loved me one,” went one line. I copied the poem out of my diary and onto a scrap of notepaper, which I passed the next day to my boyfriend Victor during English class. Our teacher, the wonderfully engaging but draconian man named Dennis McGuire, spied my surreptitious action, swooped down the aisle and snatched the note before it reached its destination in Victor’s hands. Without further ado, Mr. McGuire tucked the poem into his planner. I expected punishment. A special report on Ivanhoe? Writing “I will not pass notes in class” a hundred times? A conference with my parents? But, no punishment came. Whew! I guess the embarrassment was enough in my teacher’s eyes.

But the poem didn’t languish. Several months later, the junior/senior high school literary magazine appeared, and there between the covers was my poem! Mr. Maguire had submitted it on my behalf and suddenly I was a published poet! What a thrill to see my words—and my name—in print. And classmates were stopping me in the hallways to congratulate me and rain kudos upon me!

I never looked back. To become a poet was my destiny and it remains so these fifty-three years and 800+ published poems later. I’m still striving to live up to the man who saw in me a potential I had no idea I possessed even though he’s been gone from this Earth for two decades. His wonder never ceases.

Interview with Simon Perchik

Library Journal called him the most widely published unknown poet. However, I’ve followed Simon Perchik’s poetry for decades. His newest book, THE ROSENBLUM POEMS (Cholla Needles), is 140 poems written in triplets.

This coffee is still learning, spills
sweetens night after night
the way fireflies flavor their legs

then wait for the rippling hum

that’s not a bat

And, one of my favorites:

You keep the limp, stoop
the way this cane
lets you pretend its wood

can heal

At almost a century old, Perchik’s work certainly deals with aging, but most deeply with perception. Those triplets give me, as a reader, a sense of motion, uncertainty, even possibility.

Miriam’s Well is very happy to have an interview from the poet that answers the blogs usual three questions:

1. What is your personal/aesthetic relationship to the poetic line? That is, how do you understand it, use it, etc.
2. Do you find a relationship between words and writing and the human body? Or between your writing and your body?
3. Is there anything you dislike about being a poet?

1. Enjambment is an important concern for me.The line should have a feel so that it’s not just chopped-up prose with wide margins. Not only the reader’s breath must be considered but surprise and the tension so necessary to the text.
2. If there is a relationship I’m not aware of it. I do know that in the process of writing I often find myself agitated and often find my heart beating faster and louder. I just consider that a cost of doing business.
3. I’ve never considered myself a poet; just someone who writes poetry. In fact, except for a few close friends I never told people I wrote poetry. I think the title “poet” is something others call you, not something you call yourself by.

Review of TO CLEAVE by Barbara Rockman

Barbara Rockman’s second book, TO CLEAVE, (University of New Mexico Press) takes the ordinary world and makes it extraordinary through observation. There are peaches on a plate, deer breathing, a locket, birds, often the color red…all of these arrange the world and the self. These poems have a quality of slowing down time. It’s as if there is a usual narrative—marriage, family, children—set against a series of timeless moments.

Chamber Music

Twice this summer the thrashers
produced young in the nest
under the porch eaves, and twice
the fledglings fled.

as the cellist melds
with two violins,
i am folded
into space,

by two daughters,
twice departed,

I’ve followed Rockman’s work for several decades, and this collection feels like a sophisticated blooming of all her themes. “Absence of Wind’ moves into the magical realms of invocation-—“May the blossoms be given one more day to be praised.” These poems are intimate, the kind of quiet that makes you listen long and hard.

A beautiful volume—highly recommended.

Review of Luminosity

Poetry Review

Luminosity by Miriam Sagan
Reviewed by Karla Linn Merrifield

Miriam Sagan’s newest poetry book, Luminosity (Duck Lake Books, 2019, 80 pages), is an eye-opening poetic experience that will leave you wanting more from the poet’s distinctive modern Renaissance mind.  Most of us can remember the dramatic 2017 total solar eclipse, but I suspect none of us rendered the great celestial event into such wise, lyrical poetry as may be found in Luminosity. In “Woman, Sleeping I-20,” Sagan writes, “we are going to drive to Nebraska/ to see the total darkness” and we realize that by contemplating total darkness, we may also comprehend what it is to be bathed in total light, whether from the sun emerging from eclipse, or the moon—a recurring metaphor for light in darkness—or from Ceres and Orion’s belt in the night sky.

From the opening page, every poem brings its luminous reward. In the lead poem, “Book of Darkness,” we are told, “…light must close the cover/ on darkness.” Many are such quiet declarations we can ponder. In “A Funeral in Pawnee,” Sagan invites us to consider “the loneliness of beauty.”  She also asks questions we need to answer for ourselves. Again from “A Funeral in Pawnee,” she asks, “what did I expect/ to be betrayed?/ and what supplies/ did I prepare/ from this betrayal?” Which betrayal? What supplies?! I’m still mulling over the concepts she addresses.

Luminosity delivers many moments of pure delight. One simply must smile when reading in “every poem,” “every poem/ should have some fireflies”.

The book also touches us with bittersweet flashes. In “Dunkin’ Donuts,” we read, 
                                                         Each of us 
                                                         carries a map of the day,
                                                         sometimes creased 
                                                         in sorrow
                                                         or stained
What does your map of this day look like? Where lie the creases and stains?

Prepare to be uplifted and transported in revelatory light–and shadow–from without as well as within “your different selves.”  Miriam Sagan’s Luminosity invites you to contemplate not only the “loneliness/ of beauty,” but also “the architecture/ of suffering,” knowing, however, that “Buddha nature is everywhere” and that truth will always arise from “a fog bank/ of lies.” Luminosity is wildly, boldly illuminating.

Editor’s Note:  Luminosity is available in trade paperback for about $16.00 and as an e-book for about $4.00 from most major booksellers.