Fractal Patterns
Benoit Mandelbrot
Fractal patterns have been under our nose since the beginning of time. The mathematical relationship was only discovered in 1975 by Benoit Mandelbrot. Benoit was a mathematician and started using fractals to help him extend the concept of theoretical fractional dimensions and geometric patterns in nature. The world has never been the same since its discovery.
WHAT IS A FRACTAL PATTERN?
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. There are many uses for fractals but in this document we will be focusing on the architectural and structural benefits.
Mandelbrot Set
• Equations forming Fractal Patterns?
The simple equation Zn+1 = Zn2 + C creates part of the Mandelbrot Set. We can also find the same iconic shape in the patterns created by many other equations.
• What is the Mandelbrot Set?
It is a set of complex numbers for which the function does not diverge when iterated from. The sequence remains bounded in absolute value. It is obtained from the quadratic recurrence equation. Xn = Xn-1Xn-2
• Why is the Mandelbrot Set Useful?
The equation helps ecologists with their study of spatial ecology. Spatial ecology focuses on the study and modelling of the roles of space on ecological processes that effect ecological patterns. It also helps us to find out why space is important for ecology and conservation.
Architecture
The most beautiful and structurally sound buildings ever built were based off fractal patterns. The fractal pattern distributes the the weight of the building as well as makes it more resistant to wind and earthquakes. A common shape found in most fractal patterns is a triangle. The triangle allows for a load to be applied to one of its corners/vertices and spread the force over a greater area. This therefore reduces the overall pressure on the object. Pressure is defined as: force/area. The structure of a sponge uses the a similar triangular pattern structure. This is why a song can absorb water and can be compressed.
The tallest building in the world, The Burj Khalifa, has a conical shape made of many twisted triangles in the foundation of its design. The twisted triangles in its design allows for its construction to act like a spring under vertical compression, when the weight increases as the building gets taller. This also allows the building to be able to move slightly, horizontally, when there is strong winds or an earth quake. If the foundations were not designed this way, they would develop cracks overtime.
Some of the easiest use of fractal architecture was when then Egyptians build the first pyramid. The shape of the pyramid allowed the heavy stone blocks to be distributed over a grater area, the base of the pyramid. They were able to gain height of the pyramid by increasing the base and then adding more stone blocks on top. This is why the pyramids stood the test of time.
https://www.metropolismag.com/architecture/science-for-designers-scaling-and-fractals/
Advancements in the Medical Industry
Since the innovation of the first heart transplant and prosthetic limb there has been another major breakthrough, 3D Printed Organs. From the inner ear ossicles to skin grafting, 3D printing has the job covered. The printer consists of series of stepper motors and a single adjustable nozzle. The printer is programmed using G-code, grid coordinates, and is then able to construct a 3D object. The best part about the combination of the G-code-3D-printer technique, is that it anything modelled on SCAD software can be printed. The fractal pattern can be programmed into the printer and after some configuration, out pops your freshly printed hip replacement. The printer is perfectly suited for doing repetitive tasks, such as patterns. Which makes the 3D printing ideal for performing fractal patterns based prints.
https://www.sciencealert.com/researchers-have-just-3d-printed-a-mini-heart-using-human-tissue
More recently the fractal pattern print technique has provided a way for us to begin the project of building an artificial lung replacement. The lung consists of many networked Alveoli, which absorb oxygen though from our blood though a membrane. The network of Alveoli relates similarly to a specific fractal pattern. This means that we are now able to form a vein structure to connect the Alveoli in the lung. The advantages of lung replacements would mean that many people with lung cancer would be able to have a new pair of lungs. This may also lead to new discoveries in the treatment of brain cancer.
Establishing Order
An important thing to consider after reading this passage is that before mathematical principles were established, we regraded fractals as chaotic.
We need to establish an order before something becomes useful to us humans. This can be seen in ancient cave paintings.
The painting is an ideal way of your brain expressing its depiction it's viewed universe. Your brain can often have dreams about the previous day, wrapping up what it has learnt and any conclusions.
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