TWP Fibonacci Tree
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Fibonacci Fractal Tree
by Tree of Water and Power

Biomimicry of the most efficient solar-cell mounting system on the planet: Producing a manufacturable freestanding cell-mounting system providing greater maximum surface area at lower cost and far greater efficiency than any existing mounting system, utilizing fractals and for the first time ever, the complete infinite Fibonacci sequence. Current literature on this subject suggests that tree branches rotate based on reciprocals of single Fibonacci numbers. Our tree results in the emergence of the entire sequence as a consequence of its formalized three-size connector architecture. Read the Popular Mechanics article about our installation here.

Tree of Water and Power, Single Tree Road, Joshua Tree. All pictures unretouched, no renders, no AI


“We shape our architecture, then our architecture shapes us,” — Winston Churchill. 

Just as our designs give shape to 3D fabrication, the possibilities of 3D fabrication shape the possibilities of design; it is only because of our new ability to produce multiple complex and scaled components, that the design of this particular installation is able to be physically manifested; it may be the first architectural installation that utilizes fractals, another relatively new field which requires computers for their application. The installation is designed specifically for a single function: to increase surface area with maximum efficiency. A natural tree has the same function, as does any system in nature that uses branches to achieve the same result such as tree roots, blood vessels, lungs, or rivers. Even though there are just few differently-shaped components in this installation, the fractal-method of construction eventually results in high enough complexity to give the installation ability to perform this function, and also gives it the appearance of a biological tree or a natural branch system, even though all the branches are straight, stock-sized aluminum tubes. 

Tree of Water and Power, Single Tree Road, Joshua Tree

Function over Form

The natural tree-like appearance of the installation is not the objective in itself, it is merely the consequence of the installation being of the same efficient configuration. Naturally occurring configurations serve the same purpose - to be as efficient as possible; the objective of a rose or a tree is not to be beautiful, their objective is to perform a function using both materials and resources with maximum efficiency. Beauty is a consequence of this function. The installation may be beautiful, but it should not distract from its true value - it is an efficient machine which provides a disruptively, vastly lower cost method for increasing surface area available for photovoltaics, or indeed any application that requires increased surface area.

Tree of Water and Power concept

Fractal Construction

The installation utilizes both fractals and Leonardo Da Vinci’s ‘area preserving rule’ to achieve its configuration. A fractal is a very simple algorithm, usually a set of instructions to simply rotate, scale, repeat and not much else. A small change in these instructions, results in a very different configuration; when a computer is given these instructions to scale and rotate, it can produce very complex shapes which often resemble naturally occurring natural phenomena, even eyes and faces. If the numbers aren’t quite right, lets say 45 or 90 degree angles, the instructions would produce a shape that would ‘go around in circles’ (or squares). With the right numbers, they can produce highly complex configurations and patterns which in nature are very useful. Cicadas are an insects that emerge every 17 years to reproduce. Mathematicians now believe that this odd-numbered cycle is to avoid them reproducing with other Cicadas, ensuring that their mating periods never overlap with similar but incompatible Cicadas. This is the power of the right number, which in fractals, is an ‘unusual’ number.

Tree of Water and Power Connector, exploded view

Leonardo Da Vinci’s Influence

According to Da Vinci’s ‘area preserving rule,’ the total area of the cross sections of all the tiniest branches of a tree, are the same, or less, than the area of the cross section of the trunk - The tree’s overall thickness never increases with its height; it is only divided, meaning that the weight, volume, and mass of the tree are the same as if it were a single trunk. Another way of putting this, is that the combined ‘thickness’ or cross-sectional area of all the twigs at the ends of all the branches, together are not greater than that of the trunk. This simple concept is one of the fundamental principles for the installation. Da Vinci did not produce instructions (that we’re aware of) to describe a three-dimensional configuration, and Da Vinci did not develop the idea to produce an artificial three-dimensional tree-like structure (that we’re aware of). For that, we require fractals, which instruct the connections of the branches to ‘scale and rotate.’

Tree of Water and Power branch connector

Maximum Efficiency

The current configuration of the installation has over 1,000 termination points for over 1,000 cells, or leaves, each with a capable surface area of ~22 sq inches, or 0.15 sq ft, totaling ~155 sq ft of available surface area, including both sides of each cell, or leaf.

Existing freestanding solar installations (rigid-mounted solar panels on columns), would require an 8”+ diameter steel column, with over 6”+ deep metal reinforcement under its entire sq ft area (to keep the single large surface flat) to achieve the same result. Such structures would typically be very heavy, at least 10x more materials/mass. It would also contain scores, if not hundreds of different manufactured or custom components including screws, nuts, bolts, brackets, paint and heavy supports required to maintain the dimensional stability (flatness) of a single photovoltaic surface. The photovoltaic cells are very thin, as thin as a leaf. Six inches deep of metal reinforcement to keep a single thin membrane flat over a large single area is incredibly disproportionate. Scale dictates that this is necessary, as the membrane support may collapse under its own weight otherwise. If we change the scale, we can remove the need for membrane reinforcement entirely; just as it would be impossible to support a 150 sq ft membrane without reinforcement, but we could hold a playing card in our hands without the need for reinforcement. Scale changes the rules of physics; to us, water is a fluid substance that requires a vessel to contain; to a small insect, it is a sphere that can be carried without a vessel. These changing properties at scale are why we don’t have flowers as large as trees, they would collapse under their own weight.

The four different types of Tree of Water and Power components

Advantages over Traditional Systems

Also unlike a traditional solar mounting system which faces the same direction constantly, all the cells are distributed in all directions. Traditional solar systems have a peak output at the time of the day when it faces the sun. A distributed photovoltaic system facing in all directions means that there is no peak time, and that there is always the same number of cells facing the sun at all times during daylight. The same is not true of phototropic solar systems, which do exist. These same systems require very many more components than even a traditional installation. They also having moving parts, and depend on mechanics to maintain functionality. Existing phototropic systems weigh in excess of 1500lb to provide the same surface area as our installation which is ~150lb in weight. Flowers are phototropical, but trees are not; they rely on brute force of numbers and the many-times multiple redundancy of individual leaves to achieve the same result.

Tree of Water and Power leaf-array

A New Kind of Power Plant

A forest of these installations would be an efficient power plant, one that you could walk through safely. If the cells of the installation were light-emitting, it would be magical place which would be worthy of a tourist attraction. Again, this would not be the objective, but a consequence of its function. Still, it would be a different experience compared with today’s power-plants, which are not safe, and certainly are not beautiful in the traditional sense. It would require little to no maintenance; it would be silent, clean, safe, functional and beautiful. It would cause land to be utilizable for persons to walk amongst the trees, instead of causing it to be unusable and inaccessible, as current power-plants do. It would even have an advantage over wind-powered plants, which many people have objections to because of their effect on the landscape, property values, and even birds and wildlife.

Tree of Water and Power leaf-array, exploded view

Surplus Energy

We call the installation, The Tree of Water and Power (TWP), because it is possible to use some of the energy generated by the installations for any purpose that serves the immediate or wider environment, even generate water from the local atmosphere literally from thin air.

The availability of a large amount of surface area lends itself to other applications; if there is available energy besides solar energy which can be harvested by other means, then why not capitalize on the opportunity? In nature, even on our own bodies, a single component often performs more than one function. Our mouth for instance, is used for breathing, eating, and speaking; our ears listen, but they also provide sensory feedback for balance and orientation; our hands and other appendages have countless functions.

Tree of Water and Power branch-connector, with cross-section

“Then he showed me a river of the water of life, clear as crystal, coming from the throne of God and of the Lamb, in the middle of its street On either side of the river was the tree of life, bearing twelve kinds of fruit, yielding its fruit every month; and the leaves of the tree were for the healing of the nations.” - Revelation 22:1-2

Water Harvesting

Atmospheric Water Solutions, Florida, sells a wide spectrum of water generation systems; their smallest is a device called the Aquaboy on Amazon.com for $2000, that will produce 2-5 gallons per day of drinking water from air. The same company manufactures another installation that is capable of producing 120+ gallons per day, available with optional solar panels and battery storage for off-grid sites - this is the scale of system suitable for our own installation. It’s worth noting that the optional solar panels associated with this same installation have approximately half the photovoltaic surface area as all the solar cells on our installation.

Given that the installation can produce water from air even when there is no precipitation, it is possible to use the water to grow biological life beneath the installation, increasing soil integrity, reversing soil erosion. It would technically terraform its environment.

Ten generations of Tree of Water and Power branches and connectors

Turbine-less Wind Power

Additionally to other functions such as water-harvesting and providing light from the cells, wind energy could be harvested if the thinnest branches, or ‘stalks’ at the end of the branches were made of polyvinylidene fluoride (PVDF) connectors and tubes. PVDF is a piezoelectric polymer - it produces energy when force is applied to it. The effects of PVDF are used widely, from interplanetary space probes, to lithium batteries. Electronic scales use PVDF, as its electrical resistance changes depending on how much force is applied to it. Electric (non-flint) cigarette lighters use the same principle; they require no battery to produce a spark, force is merely applied to a material with piezo-electric qualities, and electricity is produced.

“Wind is the sacred music of the leaves; wherever and whenever the wind blows, over there leaves start their holy dancing frantically!” - Mehmet Murat İlda

Tree of Water and Power leaf-stalk connectors, exploded view

Tipping Point for Solar Adoption

The water generation, light-generation, and piezo-electric functions, are all secondary to the main objective and chosen application for the installation, which is to increase surface area for photovoltaics with maximum efficiency and lowest monetary cost possible. The combination of these potential functions is the inspiration for the name of our installation, The Tree of Water and Power. In Nobel-winning Richard Smalley’s “Top Ten Problems for Humanity for the Next 50 Years,” water and energy are the top two list items. This installation addresses both these issues, whether as a standalone unit, or a technological forest of light. The installation is designed to solve the biggest problems currently facing humanity; it is designed to help save, if the world, and the people living in it.

Existing solar ‘trees’

Cost Savings

The accepted principle of "Levelized Cost of Energy" (LCOE) for solar energy generation systems is that the average hourly output is ~23% of maximum peak output. The leaf-arrays that terminate at the end of each branch can accommodate more numerous and larger cells; the current configuration with 1000+ cells already provides twice as much photovoltaic surface area with the same area of land as traditional mounting systems. With three times the leaf cells, the photovoltaic area would in theory provide 40kW at its peak (if every cell was facing the sun at once) the average hourly output of the system is 9,200W, or 9.2kWh. Based on a lifespan of 20 years, the installation would be capable of producing 1,611,840kW, or 1.6MW. If each manufactured installation had a total cost of $15,000, that would equate to $0.0093 per kWh, or roughly a penny, over 20 years; 2 cents over 10 years; 4 cents over 5 years etc. If using the national average US price of a kWh at 12 cents as a metric, each installation would pay for itself in approximately 1.5 years. The body of the installation is likely to last indefinitely, at least 20 years, perhaps 200 years, even if the cells were updated or replaced, which they certainly would be, as photovoltaic technology advances. The branch-method of increasing surface area remains the same just as it has in nature for millions of years. There’s no paint to wear out, no bolts to rust, only an oxidized (anodized) aluminum structure that gets more oxidized over time, protecting itself from the elements and aging gracefully like an old leather chair, briefcase or statue. 100% of the mounting system is aluminum and is completely recyclable.

Tree of Water and Power, Single Tree Road, Joshua Tree


We have been living for decades in an eco-aware culture. We strive towards carbon neutrality; electric cars have become a reality, and as a society we experiment with alternative sources of energy. The energy for the bulk of our building and vehicle requirements still comes from oil, gas and coal-fired power-plants. Amongst these new sources of energy, solar has proved its value. Solar energy has ben described as the new gold rush. Photovoltaics have been developed reaching ~20% efficiency; grid parity has been achieved worldwide - the cost of a kwH produced by solar energy and grid power, is now the same. Whereas advances have occurred in photovoltaics since their inception, advancement in the field of mounting these photovoltaics, is relatively non-existent. It has been said that the people that profited most from the original gold rush are the ones that sold shovels. Howard Hughes’ family empire was built on drill bits for oil well-drilling, not oil itself. It is possible that this solar-adjacent field, is the remaining component which removes any disincentive to solar adoption. Every photovoltaic technology that arrives is replaced by the one that comes immediately after it; this installation is not sensitive to these technological changes - its function remains the same as all photovoltaics require increased surface area for maximum performance. After millions of years of evolution, we are unlikely to produce a more efficient method than this branching system.