2.1

Mathematical rationality and order beauty

The word “Mathematics” comes from the Book of Changes. “Number” is an important concept in ancient Chinese philosophy, and it has evolved into the “art” of studying mathematical laws, that is, “numeracy”. It is not only a superficial understanding of the “art” itself, but also contains philosophical thinking about the laws of change of things. The “Book of Changes” thought that everything in the world has a number. The French poet Charles Baudelaire believed that all that is noble and beautiful is the result of reason and calculation. All that is noble and beautiful, according to the French poet Charles Baudelaire, is the result of reason and calculation.Mathematical laws and the artistic sense of form are inseparable like two sides of a coin. The variable relationship caused by parameter control will inevitably form the changing law of the mathematical model, which is expressed as a pattern style with an orderly beauty ¹⁶.

Algorithmic rules can control formal aesthetics. The aesthetic intrinsic of mathematical graphics may be, as Mandelbrot put it, due to “we see the interaction between order and sudden change ¹⁷. According to Mandelbrot, the aesthetic intrinsic of mathematical graphics may be due to “we seeing the interaction between order and sudden change”Connecting the diagonals of the golden rectangle not only forms an elegant spiral shape, but also generates a Fibonacci recursive sequence formula (Fn+2=Fn+1+Fn, F1=F2=1), which constitutes the beauty of graphic order. The beauty of order, as a basic formal law, satisfies the audience’s psychological needs for “beauty”. “Orderly beauty, as one of the laws of formal beauty in artistic creation, is constantly discovered and refined in life and nature ¹⁸.” The golden ratio brings the harmony and unity of patterns, and the Fibonacci sequence allows us to see that patterns are always in an ordered and balanced visual state. These characteristics are used in this experiment.

The combination of changes in tetragonal continuous and bidirectional continuous patterns is more efficient in the application of parametric patterns. By adjusting the color, size, bones, and other pattern structural elements by parameters, the deconstruction and reconstruction of the pattern can be completed quickly, which greatly improves the application possibility of complex patterns. “Beauty lies in numbers and harmony, and the beauty of fractal graphics is the mystery of mathematics ¹⁹.”For designers, this is not only an innovation in technical means, but also an innovation in thinking.

2.2

Systematic and structural beauty

Compared with traditional patterns, systematic parametric patterns have more novelty and vitality. The integrity of the parametric pattern is based on the dynamic interpretation of the individual elements. The parametric operational logic relationship generates pattern prototypes, which are reproduced and combined with pattern bones. These prototypes will become an aesthetic whole. The patterns generated under the systematic operational logic rules of the parametric patterns show the consistency of visual style and have the ability to update quickly. Each adjustment of parameters under the same logical framework can randomly generate pattern prototypes with different forms and internal connections. Such flexibility cannot be achieved by traditional pattern design methods. The modularization of the parametric operational logic strengthens the systematicity of the pattern, that is, by changing or duplicating the modular units, the resulting unit terms generate systematic patterns ²⁰. In a constant system, due to the different arrangement and change of the modulus units, a rich combination of forms is produced, and the resulting information connotation develops to multi-dimensional with the increase of the level of the modulus change ²¹. A rich combination of forms is produced in a constant system due to the different arrangement and change of the modulus units, and the resulting information connotation develops to multi-dimensionality as the level of the modulus change increases

The superimposed application of parametric variables and generation rules makes the pattern structure present a unique visual beauty, and the parametric topology structure brings the pattern a unique form and rational beauty. By depicting the method of expressing the relationship between “point” and “line” in the form of a graph ²², the connection between points and lines is strengthened, and these modeling relationships have constructive value in exploring the spatial morphological representation of patterns.

2.3

Vitality and dynamic beauty

The parameters endow the pattern with a personalized growth trajectory, and the visual presentation of the parameterized pattern generated by the algorithm is a changeable evolution process. Small changes in algorithmic logic can be reflected in the pattern shape, and the pattern evolves into a complex pattern that spreads with neuron patterns as a trajectory, with the beauty of contingent life dynamics. The parametric pattern thus forms a set of “growth systems”. Constantly mutating into new styles.

Different from traditional patterns, the topological and abstract nature of parametric patterns makes them have multi-dimensional derivative forms, that is, morphological styles in different dimensions of patterns are obtained based on parameter changes and logical organization ²³. Vital signs determine the dynamic beauty of parametric patterns. Ramazo proposed: “The most beautiful and most vital part of the work is that it can express movement. “ Patterns with dynamic aesthetics can attract people’s attention and stimulate visual perception. This is because the dynamic form is more likely to arouse the excitability of the human cerebral cortex, mobilize the sensory response, and cause a pleasant physiological-psychological resonance. Parametric patterns are based on the beauty of life dynamics based on mathematical regularity and are destined to have stronger visual communication value.

3.1

Morphological experiment of multi-line offset

Multi-line offset is divided into equidistant broken line offset and non-equidistant multi-line offset. These two forms use lines as the main elements to generate patterns. Linear patterns have distinct personality and are full of changes, and are the best means to express patterns such as curved, straight, thick, thin, long, and short. The linear composition of the Bird-and-Insect Script is highly compatible with the multi-line offset form, which is very suitable for experiments on this intelligent pattern generation method. The specific process is as follows:

Experimental steps of equidistant disconnection offset

The Bird-and-Insect Script pattern generated by the experiment can be adjusted and controlled for the shape elements such as the thickness, number of layers, range, precision, segment value, peripheral curve value, thickness, smoothness, gradient coloring order, etc. of the disconnection offset, so as to achieve the optimal shape (Figure 2, Figure 3). These linear pattern prototypes have strong dynamic vitality, showing good applicability in later cultural and creative product design.

Figure 2.

Isometric break offset logic build frame.

Figure 3.

Bird-and-Insect script pattern for isometric break offset patterns.

Non-equidistant multi-line migration experimental steps

The Bird-and-Insect Script pattern generated by the experiment can be adjusted and controlled for the multi-line offset layers, range, precision, thickness, smoothness, gradient coloring order and other shape factors, so as to achieve the optimal shape (Figure 4, Figure 5). The linear pattern prototype has a strong sense of order, and good visual aesthetics.

Figure 4.

Non-equidistant multi-line offset logic construction framework.

Figure 5.

Bird-and-Insect Script pattern for unequally spaced multi-line offset patterns.

3.2

The experiment of obtaining the shape of the variable of line length and rotation value

The Bird-and-Insect Script pattern experiment, which uses line length and rotation as variables to obtain the shape, pursues the beauty of linear divergence. This experimental idea draws on the principle of linear divergence in parametric architectural design to create a sense of space and movement in the font pattern. E.H. Gombrich pointed out that in the process of pattern appreciation, the eyes are forced to move along fixed, redundant repeating lines, and this visual perception mechanism creates a sense of spatial chaos in the pattern. The Bird-and-Insect Script pattern generated by the experiment can be adjusted and controlled for the shape factors such as line length, line rotation angle, line thickness, smoothness, color gradient, etc., so as to achieve the optimal shape (Figure 6, Figure 7). These linear patterns The prototype has a complex sense of space, and the visual effects have a certain sense of technology.

Figure 6.

The logical construction principle of obtaining the shape with the line length and rotation value as variables.

Figure 7.

The pattern of bird and insect book with variable line length and rotation value to obtain the shape.

3.3

Morphological experiment of grayscale interference

The experiment of grayscale interference to obtain the shape mainly pursues the accidental effect of the Bird-and-Insect Script pattern, and the font-based pattern is diffused and extended outwards. The focus of the experiment is to set a curve function <Graph Mapper> to control the density of points on the concave-convex surface so as to control the density of points on both the concave-convex surface and the plane. Use <Contour> to generate different numbers of uneven contour lines, use <Boundary Surfaces> to create a flat shape from a series of edge contour lines, and use <Scale NU> to proportionally scale the flat shape to finally form equal heights Linear forms (Figure 8, Figure 9), these linear pattern prototypes have flowing contingency, and the visual effect has a strong anti-counterfeiting function.

Figure 8.

Grayscale interference acquisition morphological logic construction framework.

Figure 9.

Bird-and-Insect Script Pattern of Grayscale Interference Acquisition Morphology.

3.4

Morphological experiment of point form

The different arrangements and combinations of dots produce the laws of beauty. The size, quantity, position, movement, light and shade of dots and other modeling elements have derived the ever-changing visual forms. The point-shape Bird-and-Insect Script parameterized pattern experiment starts from three-dimensional space, combines the curvature changes of each point and the surface, and controls the size value of the point shape through the numerical field. In addition, through the color value gradient, the color change of the line is controlled by a nonlinear function, that is, the color gradient value is affected by the thickness value of the line. Finally, point patterns with different angles, colors, virtual and real, and density are obtained through calculation (Figure 10, Figure 11). These linear pattern prototypes have rich color changes, and the visual effect is similar to the “pointillism” school of painting²⁴.

Figure 10.

Morphological logic construction framework.

Figure 11.

Bird-and-Insect script pattern of dot pattern.

3.5

Conformal design and application of parameterized cultural and creative patterns

The pattern prototype obtained from the experiment can better participate in the design application through conformalization, and the conformalization will be completed through two steps of pattern cutting and pattern mapping flow (Fig 12). After cutting the pattern prototype, the pattern flows from the source surface to the desired object, so as to complete the conformal application of the parametric pattern in cultural and creative design. Through related operations, the horizontal position, cutting style, mapping direction, and size of the pattern can be adjusted according to the shape of the object. Specific steps are as follows:

Figure 12.

Bird-and-Insect script parametric cultural and creative pattern conformal logic construction framework.

Figure 13.

Application of Bird-and-Insect script pattern conformalization.