Standing before these two trees on a unseasonably warm autumn day, I am struck by the intricate patterns of their fallen leaves. Against the vibrant green of the grass, the golden leaves form halos around the trunks, as if nature herself were sketching mandalas. There’s something profoundly mathematical about these arrangements—a quiet order amidst what might initially seem like chaos.
The first tree, its barren branches reaching skyward, stands on a carpet of yellow that radiates outward in near-perfect symmetry. The leaves have fallen in such a way that their density decreases as the distance from the trunk increases. It reminds me of the inverse square law—a principle in physics that governs how light, gravity, and sound diminish with distance. Here, instead of energy dispersing, it’s the leaves thinning out, their graceful scatter dictated by the wind’s whims and gravity’s pull. There’s an undeniable harmony in this seemingly random process, a convergence of natural forces creating an elegant gradient.
Stewart Park, Ithaca, New York
The second tree presents a different story, yet one equally mesmerizing. Its leaves, still clinging in part to the branches, form a looser ring at the base. The distribution is uneven, hinting at prevailing winds or the sheltering influence of nearby buildings. But even in this asymmetry, I see fractals—the self-similar patterns that repeat at different scales throughout nature. Look closely, and you’ll notice clusters of leaves mimicking the broader structure of the canopy above. It’s as if the tree’s essence is echoed in the ground below, a reminder of how deeply interconnected every part of a system can be.
Robinia pseudoacacia, commonly known as the black locust
These patterns invite reflection on the mathematical principles governing our world. Fibonacci sequences, golden ratios, and fractals—abstract concepts are not confined to textbooks. They are etched into the fabric of existence, visible in the spiral of a sunflower’s seeds, the curve of a nautilus shell, and the fall of leaves beneath a tree. Even the chaos of autumn is underpinned by order, a dance choreographed by countless variables: the angle of the branches, the strength of the wind, the moisture in the air.
I find myself wondering about the unseen forces at play. How many leaves fell straight down, obeying only gravity? How many were carried aloft by a breeze before settling farther afield? Could we model these patterns with algorithms, tracing the arc of each leaf’s descent? Would the data reveal a perfect equation, or would it remind us that some mysteries resist full comprehension?
As I stand here, I feel a deep gratitude for these natural equations. They ground me in the present moment while also connecting me to the infinite. The pattern of leaf fall is a reminder of life’s balance: chaos and order, randomness and structure, fleeting moments and timeless principles. The trees, now shedding their golden crowns, invite me to pause, observe, and marvel at the beautiful mathematics of autumn.
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Copyright 2025 All Rights Reserved Michael Stephen Wills
Taughannock Falls, a majestic 215-foot waterfall, showcases nature’s beauty and power, intertwining geological history with vibrant ecosystems in New York.
Introduction Nestled in the heart of the Finger Lakes region of New York, Taughannock Falls stands as a testament to the delicate balance of power and beauty in nature. This iconic waterfall plunges 215 feet—one of the tallest single-drop waterfalls east of the Rocky Mountains—into a gorge whose story is written in stone. The park surrounding this natural wonder offers a symphony of sights, from towering cliffs to lush greenery, inviting visitors to explore its ancient secrets and vibrant life.
View of taughannock Falls from the South Rim Trail. Taughannock Falls New York State Park, Trumansburg, Tompkins County, Finger Lakes Region
A Story Written in Stone The rocks of Taughannock Falls tell a story that stretches back 380 million years to the Devonian Period, a time when the region was submerged beneath a shallow inland sea. Layer upon layer of shale, sandstone, and limestone formed as sediment settled to the ocean floor, preserving the fossils of marine life that once thrived here. These rocks have endured the passage of eons, but the gorge itself is a far more recent creation.
Limestone Steps on the South Rim Trail descend to the gorge floor.
It was the retreat of the mighty Laurentide Ice Sheet, approximately 10,000 years ago, that set the stage for Taughannock’s grandeur. As glaciers melted, torrents of water carved the U-shaped valleys that now cradle the Finger Lakes. Taughannock Creek, a tributary of Cayuga Lake, began its work, etching its path through ancient rock, sculpting the gorge we see today. In just 10,000 years—a fleeting moment in geological time—the relentless force of water carved its way 3/4 of a mile upstream, creating the awe-inspiring chasm and waterfall that continue to evolve even now.
Taughannock Creek carved this landscape over thousands of years.
The Gorge’s Living Tapestry Beyond its geological wonders, Taughannock Falls State Park bursts with life. Along the North and South Rim Trails, Eastern Hemlocks (Tsuga canadensis) stand tall, their evergreen branches weaving shadows that dance across stone stairways and forest floors. These silent sentinels are habitats for myriad creatures and protectors of the delicate ecosystem.
Wildflowers were planted by park staff at the Falls Overlook. The bright yellow of Black-eyed Susans (Rudbeckia hirta) and the vibrant purple of Coneflowers (Echinacea purpurea) attract bees and butterflies, their nectar fueling the intricate web of life that thrives here. Along the trail, on the forest floor, mosses and ferns cling to rocks, softening the edges of the gorge with their verdant touch.
Cone FlowersCone Flowers gone to seedFrom a walk around Taughannock Falls State Park “Rim Trails” October 22nd, 2024. Trumansburg, Tompkins County, Finger Lakes Region, New York State.
The Fall’s Eternal Dance At the heart of the park is the waterfall itself, its roar both a hymn and a whisper of time’s passage. The view from the North Rim Trail reveals the waterfall framed by steep cliffs, their striations like pages in a book written by water, wind, and time. The plunge pool below, shimmering in sunlight, seems almost sacred—a place where the forces of nature meet in harmony.
Viewed from the North Rim Trail on a summer morning. Taughannock Falls New York State Park, Trumansburg, Tompkins County, Finger Lakes Region
Even as we marvel at its beauty, the falls are a reminder of the earth’s constant transformation. Each drop of water that cascades down the cliff face carries away tiny fragments of rock, continuing the slow, deliberate work of reshaping the land. What we witness today is but one moment in an ongoing process—a fleeting glimpse of a masterpiece in progress.
A Place of Wonder To stand at the edge of Taughannock Falls is to feel both small and connected. The cliffs, formed over hundreds of millions of years, whisper of ancient seas and forgotten worlds. The gorge, carved in the blink of an eye by geological standards, speaks to the power of water and time. And the vibrant life that fills the park reminds us of nature’s resilience and beauty.
As the sun filters through the trees, illuminating the mist that rises from the falls, it’s easy to believe that this place holds magic. Perhaps it’s in the way the water sparkles like diamonds in the sunlight or the way the breeze carries the scent of pine and earth. Or maybe it’s in the knowledge that here, in this park, we are witnesses to a story billions of years in the making.
Conclusion Taughannock Falls State Park is a place of wonder where geology, ecology, and history converge. It invites us to reflect on the immense forces that shape our world and to cherish the fleeting beauty of each moment. Whether you come to marvel at the towering waterfall, walk among the hemlocks, or simply stand in awe of the gorge, Taughannock Falls leaves an indelible mark on the heart—a reminder of nature’s power, resilience, and enduring grace.
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Copyright 2024 All Rights Reserved Michael Stephen Wills
Discover the timeless beauty of two towering Cottonwood trees along the shores of Cayuga Lake. Explore their natural history, cultural significance, and how they’ve shaped the landscape of Stewart Park for generations.
Walking with Pam in Stewart Park, the shores of Cayuga Lake shimmer under the bright September sun, offering a serene setting for reflection. Ahead, two towering Cottonwood trees stand in quiet majesty, their branches spreading wide, casting long shadows over the grass and walkway. Drawn toward them, I find myself in awe of their presence—these two trees, ancient sentinels by the water, who have silently borne witness to the changing world around them.
View Facing East/Southeast, September 10, 2024
Cottonwoods, scientifically known as Populus deltoides, are members of the poplar family and are among the tallest trees in North America. The ones before me have thrived for decades, their thick, furrowed trunks a testament to the endurance of life on the edge of the lake. It’s remarkable to think of all the storms and seasons they’ve weathered—their roots digging deep into the moist earth, nourished by the lake’s constant ebb and flow. I feel as though these trees, standing side by side, companions, connected through the unseen networks of roots beneath the soil. Their relationship to one another seems profound, they have grown up together, providing support and strength as they aged. Their canopies overlapping as though embracing one another.
There’s an undeniable symmetry to their relationship, both in form and function. One can imagine them as silent witnesses to the changing landscape around them—the gradual expansion of the park, the families that come and go, the laughter of children playing nearby, and the quiet conversations of couples walking hand in hand. These trees have become part of the fabric of Stewart Park, deeply entwined with the human history that unfolds here every day.
View Facing East, September 10, 2024
The branches reach skyward, their leaves shimmering in the breeze, producing the characteristic fluttering sound of Cottonwoods. There’s something deeply soothing about this rustling—the way the wind seems to dance through the leaves, creating a rhythm that feels eternal. It reminds me that these trees have long been part of human experience, a backdrop to countless strolls, picnics, and quiet moments of contemplation here at Stewart Park.
Cottonwoods are fast-growing, often found near bodies of water where their shallow roots can tap into consistent moisture. And yet, their rapid growth comes with a trade-off; their wood is soft and brittle, prone to breaking in high winds. But in Stewart Park, these two trees have found a perfect balance, their large, sweeping canopies offering shade and shelter without suffering too much damage from the storms that blow through the Finger Lakes. Their resilience is remarkable—a reminder of nature’s ability to thrive in challenging conditions.
Historically, Cottonwoods have played a significant role in the lives of the people who encountered them. Native Americans once used the bark for medicinal purposes and fashioned the wood into canoes. Early settlers appreciated the trees for their rapid growth and ability to provide shade and timber in otherwise open expanses of the Midwest and Northeast. Even today, their legacy endures as they continue to offer shade and shelter, albeit more for leisure than for survival.
I notice how the pathway itself bends gently to accommodate the Cottonwoods. The paved trail, so clearly designed with these majestic trees in mind, arcs around their broad bases as if to honor their presence. In a world where nature is so often bent to human will, it’s refreshing to see this small, quiet gesture of deference—a reminder that in our modern parks, nature can sometimes lead the way.
View Facing West, June 25, 2024
The path doesn’t cut through or impose upon these trees. Instead, it respects their claim to the land, curving around them in a way that feels organic, almost reverent. The roots of these Cottonwoods must reach far beyond what I can see, extending outward in all directions beneath the soil, beneath the path itself. It’s as though the trees and the human-made elements of the park have reached a compromise—a harmonious balance where both can coexist without either having to sacrifice too much.
In their wisdom, the planners of this park understood that these trees had already laid their claim long before the park’s paths were laid out. It’s a small but profound testament to the enduring power of nature and the foresight of those who designed this space. As I walk along the path, I feel the subtle shift in the landscape—the way the curve of the trail encourages a more leisurely pace, inviting visitors to pause for a moment and take in the grandeur of these ancient trees.
The curve itself creates a sense of flow, as if the path is gently nudging us toward a deeper appreciation of the Cottonwoods. There’s no rush here. The trees stand in their place, rooted and steadfast, while we are invited to move around them, to change our course slightly in order to make space for something larger than ourselves. The path becomes a metaphor for our relationship with nature—we must sometimes bend and yield to its greater forces, rather than insist on our own straight and rigid lines.
This curved path speaks to the broader theme of adaptability—how both nature and humanity have learned to accommodate one another. The Cottonwoods have withstood the test of time, their roots dug deep into the soil, while we have found ways to move alongside them, adjusting our course to allow for their growth. It’s a quiet but powerful reminder of the importance of coexistence and respect, of making space for the natural world rather than always seeking to dominate it.
As we pass by, I notice the texture of their bark—deeply furrowed and rough, a tactile reminder of the passage of time. Each ridge and crevice holds the story of countless seasons—of dry summers, harsh winters, and everything in between. I reach out and touch one of the trunks, feeling the coolness of the bark under my hand. There’s a vitality here that can only be sensed up close, a quiet hum of life that pulses just beneath the surface.
Yet, despite their imposing size and age, the Cottonwoods remain humble in their role. They do not demand attention like a flowering dogwood or a brightly colored maple. Instead, they offer something more enduring—a quiet, steady presence that provides shelter and shade without fanfare. Their leaves turn a brilliant yellow in autumn, adding to the kaleidoscope of colors that make up the Finger Lakes’ fall landscape. But even in winter, when the leaves are gone, their bare branches stand against the cold sky, offering a stark beauty all their own.
As I step back to take in the full view of these two Cottonwoods, I am filled with a sense of gratitude. Their lives, so intimately tied to this place, remind me of the interconnectedness of all living things—the way nature, time, and humanity overlap in ways both seen and unseen. These trees, growing together on the shores of Cayuga Lake, are not just part of the landscape—they are part of the story of Stewart Park and, in a broader sense, the story of this region. They remind me that, like them, we are all shaped by our surroundings, by the people and places that stand beside us as we grow. And in that way, we are never truly alone.
Copyright 2024 Michael Stephen Wills All Rights Reserved
Michael Stephen Wills Photography 