Design Related To Math: Exploring The Visual Secrets

Indeed, graphic design doesn’t require so much math but there is some graphic design related to math that stands as the foundation that visually appealing design sits upon. Graphic design is a creative process that sometimes requires mathematical calculations to create that professional-looking design that most graphic designers consider to be the hard part of design

For instance, graphic designers find the renowned Fibonacci Sequence to be straining and difficult to achieve but no matter how challenging it may appear, when executed proficiently, one experiences a sense of accomplishment and pride simply for attempting.

Let’s figure out how graphic design related to math really works, we can analyze them and see how they impact graphic design and every other aspect of life around us.

Here Are Various Design Related to Math

Fractals

At their core, fractals are infinitely complex patterns that are self-similar across different scales. This is simply done by doing a math equation over and over again to create this design pattern. This means that no matter how much you zoom in or out on a fractal, you’ll continue to see similar patterns repeating themselves. The concept of self-similarity lies at the heart of fractal geometry and distinguishes fractals from other geometric shapes.

In 1975 Benoit Mandelbrot 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. 

Fractals can be found in almost all areas of nature. Tree branches, snowflakes, and lightning bolts for example have jagged lines that repeat themselves in smaller sections, another is snowflakes.

Each snowflake has its own unique design but follows the same patterns.

Using a recurring pattern with the help of a mathematical equation that allows patterns to repeat themselves on different scales.

Characteristics of fractal design

Fractals come in different forms, shapes, and sizes but it has a holistic characteristic that is evident in all of their parts whether big or small. Here are the various characteristics that will help you identify a fractal pattern when next you see one. 

Infinite repetition

Fractals exhibit self-similar patterns at increasingly smaller scales, meaning that as you zoom in on a fractal, you will continue to see similar patterns repeating infinitely. This property is also known as “infinite complexity” because no matter how much you zoom in, you’ll always find more intricate details.

Smaller similar pattern

Fractals possess the property of self-similarity, where parts of the fractal resemble the whole, or smaller portions of the fractal resemble larger portions of it. This recursive property is what creates the intricate, repeating patterns seen in fractals.

Irregular

Fractals often have irregular or rough shapes, rather than smooth and regular geometric shapes like circles or squares. This irregularity contributes to the unique and complex appearance of fractals, allowing them to represent natural phenomena with high fidelity.

Simplicity

in the context of fractals refers to the fact that despite their complex and intricate appearance, the generation rules or algorithms that create fractals are often based on simple mathematical equations or iterative processes. Even though the resulting patterns may appear highly detailed and complex, the underlying rules governing their formation can be expressed concisely.

For example, the famous Mandelbrot set, one of the most well-known fractals, is generated using a simple iterative formula involving complex numbers.

Tessellations

Tessellation is the use of shapes to cover a surface or art design without leaving a gap in between. tessellation can be done. By using simple geometric shapes like squares, triangles, and hexagons, (circles don’t tessellate because of the gap they create in between. However, you can use curved diamond shapes to fill up the gap, or much more complex or irregular shapes (such as stylized birds or fish) that have been designed to fit together neatly in a repeating pattern.

Tessellation is a design related to math because it uses the math equation to identify if a shape will tessellate or not and this is done by finding out if the vertices (corners) should all form. 360-degree angle in order to tessellate.

Tessellation can be considered both math and graphic design because it uses math formulas to make graphic design patterns and 3-Dimensional graphics. However, the core study of tessellation can be found under Euclidean geometry on the Euclidean plane.

There are three categories of tessellation.  A regular tessellation is made up of simple repetitive regular polygons of the same size and position. (There are only three types of regular tessellations consisting of equilateral triangles, squares, and regular hexagons, respectively). 

A vertex is defined as the point where the shapes join together. A semi-regular, or an Archimedean tessellation, is made up of more than one type of regular polygon in an isogonal arrangement. That is, The pattern at each vertex is identical. There are right semi-regular tessellations. 

Fibonacci Spiral and Golden Ratio

The Fibonacci Spiral is the key secret behind why some art is just so mesmerizing and appealing to the human brain. The incredible math in graphic design was invented by Leonardo Fibonacci an Italian mathematician. The Fibonacci Spiral also as “The Phi Ratio”  or “The Divine Proportion” is a concept that uses a series of numbers – (0,1,1,2,3,5,8,13,21 and so on) to create visually striking designs

The golden ratio follows a similar pattern of using a mathematical ratio also known as The Golden Spiral Ratio, which uses a a ratio of 1.618 as the secret code of its design pattern. And all this can be done right inside a square

This sequence has fascinated mathematicians for centuries due to its profound mathematical properties which can be applied in graphic design as well can be found in man-made objects, buildings, and creations of nature.

Penrose Tiling

Named after Roger Penrose 1970s, Penrose tiling is a non-periodic tiling pattern. Unlike regular periodic tilings, such as those made by squares or hexagons, Penrose tilings are made up of a set of shapes that can be arranged in various combinations without repeating the pattern. These shapes consist of two types of rhombi, or diamond-like polygons, which are referred to as “kites” and “darts.”

What adds to the allure of Penrose tiling is its ability to exhibit rotational and reflection symmetries despite lacking translational symmetry. In a Penrose tile arrangement, you can rotate it around a central axis, and it will retain its original appearance. However, if you attempt to shift it horizontally, the pattern will not align. 

Penrose tiling is a type of design related to math that requires a rich amount of time at hand and good mathematical knowledge to create this type of pattern. But the final result looks really stunning.

Escher-like Optical Illusions

Maurits Cornelis Escher’s artwork is a typical example of the more you look the more confused you get. Escher optical illusion creates incredible artwork by combining mathematics, visual design and geometry to create artwork that challenges viewers’ perceptions of space, depth, and reality.

Escher utilized fundamental geometric patterns in his tessellations, employing reflections, glide reflections, translations, and rotations to create a diverse array of designs. He further embellished these patterns by transforming basic shapes into animals, birds, and various figures, ensuring that these distortions maintained the three, four, or six-fold symmetry of the original pattern to uphold the tessellation. The result is striking and has an aesthetically pleasing effect.

Möbius Strips

The Möbius strip is a fascinating mathematical object that has intrigued mathematicians, artists, and thinkers for centuries. Named after the German mathematician August Ferdinand Möbius, this strip defies conventional geometry and challenges our understanding of space and dimensionality.

A Möbius strip is a two-dimensional surface with only one side and one boundary. It is constructed by taking a long strip of paper, giving it a half-twist, and then joining the ends together. The result is a loop with a single surface and a single edge. This seemingly simple object has some truly remarkable properties that have captured the imagination of mathematicians and artists alike. 

Mobius inspiration can be commonly found on architectural buildings.

It also inspires the recycling sign which creates a healthier planet for ourselves and future generations.

The Möbius strip’s most striking property is its one-sidedness; unlike a traditional loop, it has only one side. Drawing a line along its center without lifting the pencil covers both “sides.” It also has a single edge and surface, and is non-orientable, lacking a defined “up” or “down.” This property is significant in mathematics, particularly in topology.

Sierpinski Triangle

The Sierpinski Triangle is a fractal named after the Polish mathematician Wacław Sierpiński. It is a self-replicating pattern that occurs by recursively dividing a triangle into smaller equilateral triangles. This process is repeated with each smaller triangle, creating an infinite pattern of triangles within triangles. 

The Sierpinski Triangle is a classic example of a fractal, displaying self-similarity at different scales. It has applications in mathematics, computer graphics, and even art and design.

Platonic Solids

The Platonic solids are geometric shapes with the same surfaces and properties when put together. It said that these unique shapes were discovered by Plato a Greek philosopher however, critics claim Pythagoras to have discovered three of the solids- the cube, tetrahedron, and dodecahedron and then Plato came in and discovered the remaining two – the octahedron and icosahedron which sums total of five platonic solids.

So, what’s amazing about these shapes? It is said that Pythagoras went to ancient Egypt in 535 BC to study with other priests about the power of platonic knowledge. These shapes have become a foundation of disciplines like graphic design and art and have been used to create meaningful visual communication.

It’s also important to know that the platonic solids represent the five building blocks of the universe which represent fire, water, earth, air and universe (it could also be called ether or prana).

This platonic solid has interesting criteria, they are created with the same edge length, they have the same size of the same face, the same angle, and all the points or vertices of each shape fit perfectly inside a sphere. These are apparently the only shapes known to us up till now that fit this criteria which is a great representation of perfect balance and harmony.

Voronoi Diagrams

Named after the mathematician Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation. Voronoi Diagrams are diagrams that partition a plane into regions based on the proximity to a specified set of points. It could be considered similar to a tessellation but follows a different pattern process.

Voronoi diagram is one of those mathematical oddities, like fractals and Fibonacci spirals, that turn up frequently in our natural world. 

It is easy to make the Voronoi diagram. just sprinkle some random point (sites) across a plane, try connecting these sites with a line (linking each point to those which are closest to it), and then bisect each of these lines with a perpendicular.

The Voronoi diagram can be found on nature’s creatures like the body of a giraffe, you could see a similar pattern on turtle shells, dried desert mud, aerial view of your neighborhood, leaves and so many other areas of man-made and nature’s creation.

Voronoi pattern found in plants

Geometric Constructions

Geometric construction is the use of geometry to create shapes like circles, triangles, squares, polygons, rectangles, heptagons, octagons, nonagons, decagons, dodecagons, rhombus, parallelogram,s, and so on. Constructing these shapes uses a precise mathematical calculation to achieve an accurate proportion in their design.

These geometric shapes are crucial when designing posters, logos, motion design, and other design materials. According to Euclid the father of geometry, mathematics can be used to explain art and design. We can see how the various designs related to mathematics add to stunning visuals. This is evident with the Fibonacci Spiral and Golden Ratio which uses math equations to create appealing visual design.

Geometric patterns in graphic design use shapes and lines repeatedly to create eye-catching, original designs. These patterns, ranging from basic shapes to complex digital designs, are effective in capturing attention due to the natural attraction of the human eye to geometric forms. Pairing geometric patterns with vibrant color schemes can result in engaging visual content that leverages shape psychology and artistic principles.

Frequently Asked Questions About Design Related To Math