Fractal Geometry in Design: What You Need to Know
Fractal geometry in design is the use of Fractals to create or improve designs. Fractals are geometric shapes that can be split into parts, each of which is a smaller copy of the whole. Fractal geometry in design can be used to create more efficient designs, or to make the design more aesthetically pleasing. Fractal geometry can also be used to create patterns that are more organic and natural-looking. Fractals can be used in a variety of design fields, including architecture, web design, and product design.
Origin
Mandelbrot’s set. Image Source: Sciencemusings.com
In 1975 Benoit Mandlebrot coined the term fractals. Mandelbrot defined a fractal as: “A set whose fractal dimension is strictly greater than its topological dimension.” Mandelbrot states that "ideal" geometric figures for representing natural objects must contain "copies" of themselves or "similar" copies of each part, as these occur in nature itself. He proposes that it can be observed by continuous enlargement. Mandelbrot is termed as the father or pioneer of fractal geometry. Most of the principles of this interdisciplinary discipline regiment of mathematics and physics already existed, not because he created fractal geometry, but, of course, because as he put them together in a single coherent discipline. Please call his name.
Properties
Never-ending
The fractal patterns are never-ending, which means on zooming further, the pattern keeps repeating endlessly incessantly.
Self-similar
The basic structure of the fractal pattern keeps repeating itself to form a pattern.
Irregular
The fractal pattern on a large scale is generally irregular.
Fractional Dimension
The most striking feature of fractal patterns is that they are somewhere in between normal 1D, 2D, or 3D shapes.
Simplicity
Despite the complexity of the fractal structure, the form comes from a very simple core definition. A small list of mathematical numbers can capture the shape of a fractal. These maps show exactly how small copies of the fractals are arranged to make the whole fractal larger. Fractals start with simple geometric objects and rules for modifying objects. This ultimately leads to objects that are very complex and have non-integer dimensions.
Types of Fractals
Natural Fractals
Spiral Aloe vera. Image Source: Treehugger.com
Fractals are ubiquitous in nature and span various scales. The same pattern can be found many times, from the small effects of blood vessels and neurons to the impact of trees, lightning, and river networks. All of these patterns, regardless of size, are formed by repeating a simple branching process.
Geometric Fractals
You can create pure geometric fractals by repeating a simple process. The Sierpinski triangle is create through the repeated removal of the middle triangle from the previous generation. The number of colored triangles increases by a factor such as 3, 1, 3, 9, 27, 81, 243, 729 for each step. Koch curve is another great example of geometric fractals.
Algebraic (Abstract) Fractals
You can also calculate simple equations over and over to create fractals. Equations need to be calculated thousands or millions of times, so you need a computer to look them up. It is no coincidence that the Mandelbrot set was discovered in 1980, shortly after the invention of the personal computer.
Multifractals
Cyclic fractal. Image Source: Cgtrader.com
Multi-fractal is a generalization of the fractal, characterized by a continuous spectrum of dimensions rather than a single dimension.
Examples
Fractals were used hundreds of years, perhaps thousands of years ago, but were not called fractals. They were arts and crafts, carpet, and painted floor and ceiling designs, and designs found in many objects used in everyday life. For example, clouds, mountain ranges, lightning, bolts, coastlines, and snowflakes.
A Koch curve
Koch curve. Image Source: Larryriddle.agnesscott.org
A Koch curve-based representation of a nominally flat surface can be constructed similarly by iteratively segmenting each line in a serrated pattern of segments at a particular angle. Swedish mathematician Niels von Koch published his eponymous fractal in 1906. It starts with an equilateral triangle. Based on the central third, three new equilateral triangles are created on each side and removed to form six-pointed stars.
Sierpinski’s triangle
Sierpinski triangles Image Source: Oftenpaper.net
Sierpinski triangles, also known as Sierpinski gaskets or Sierpinski sieves, are a fractal-attractive solid set in which the overall shape of an equilateral triangle is recursively subdivided into smaller equilateral triangles. Is. You can divide the Sierpinski triangle into three self-similar parts (n = 3) and magnify each with a factor of m = 2 to get the entire triangle. The formula for dimension d is n = m ^ d. Where n is the number of self-similar parts and m is the magnification.
Application in Design
Fractals in Architecture
Fractals in architecture. Image Source: Newearth.university
When an architect designs a fractal geometry, he tends to use it aesthetically from to, and he tends to create a generally recognizable decorative, complex pattern. This led to the design of the rack façade using fractal geometry. The fractal involvement in building skin design is more pronounced than the architectural form of the masses and spaces. Patterns generated with fractal geometry are mainly used in skin design. This poses the risk that the fractal geometry will degenerate to the surface and be applied directly and superficially. Fractal geometry is applied to architectural design. It is widely used to study the fractal structure of cities; it succeeded in constructing geometry and design.
Fractal analysis of the architecture can be performed in two steps:
• Small-scale analysis of building self-similarity (for example, analysis of a single building)
(Components that repeat on different scales)
• Large-scale analysis (such as city-level analysis) and Box count dimension (to determine)
Fractal dimension of the building)
Fractals in Fashion
World of fractal fashion. Image Source: Annekadotes.com
Since its discovery, fashion designers have used the visual potential of geometric fractals to create outstanding effects. Dutch designer Iris van Herpen is not afraid of experimentation and innovation. Her radically original work often has an organic theme and reflects her observations of nature and the human body. Their infamous skeletal dresses are reminiscent of the self-similar fractal patterns found in our biological composition.
Van Helpen's crystallized works are inspired by the study of this basic scientific process of liquid-to-crystal conversion, exploring the beauty found in the laboratory. The tree pattern is one of the most prominent examples of fractals in nature. More than 500 years ago, Leonardo da Vinci realized that there was something more in the swirling chaos of trees. He saw the branches split with mathematical precision.
Zuhair Murad. Image Source: Annekadotes.com
Lebanese designer Zhuail Murad's Enchanted Forest collection takes advantage of this self-similarity of Haute Couture design, with repeating patterns of sparse branches creating an aerial elegance that matches the essence of his brand.
3D Modeling of Fractals
Fractal polyhedra. Image Source: Georgehart.com
Fractals are self-replicating patterns, and thus 3D modeling makes it easier to create such designs. The only thing that needs to be done is to design a primary structure. The next step is to keep repeating them on a specific rotation angle, distance, and dimension. There are different 3d design software available that one can use to prepare fractal designs but most of the commonly available programs are either complex or expensive and not everyone can be able to afford them. But there are other easy to use and powerful 3D modeling software like SelfCAD. With SelfCAD, users can model, sculpt, modify, and even prepare their fractals for 3D printing using the in-built slicer hence users doesn't have to switch to other programs. There is also a powerful rendering engine that you can download and use it to generate realistic renders of your designs after you are done with 3D modeling. With SelfCAD, you can get started easily as the tools are well arranged in the interface and most of those tools are reusable too.
The software has interesting and powerful features like the freehand drawing and sketching tools that makes it easier to 3D draw and sketch your fractals with ease and hence bring your ideas to life. There is an image to 3D feature too that is handy especially if you have an image of your 2D drawing that you would like to create a 3D model from it. You can import all kinds of images using the reference image tool, trace around them using the freehand drawing and sketching features and turn them into a 3D model at a click of a button.
There are also a lot of interactive tutorials that one can use to learn 3D modeling with much ease. The software is also affordable and you can use it to prepare both simple and complex fractals easily.
Enjoy powerful modeling, rendering, and 3D printing tools without the steep learning curve.
Need to learn 3D modeling software? Get started with interactive tutorials.