## The Magic of Math in MidJourney Prompts: Parametric Paint Strokes

### Introduction

Welcome to a captivating realm where mathematics intertwines with art, and MidJourney prompts become canvases for creative expression. In this blog post, I’ll delve into the interesting technique I employ to craft unique and captivating images using a remarkable parametric math formula. Join me to explore the beauty that emerges when numbers and creativity merge.

### The Process

A human hand can yield a paintbrush as an instrument, and draw curves of influence to form the image. Here I apply math as a kind of paintbrush. I use a parametric curve mathematical formula to draw a hyper curve of influence upon the form of the image. I’ve used this technique, combined with with unique methods of promoting, to create entire collections of AI generated image art, including my Gamma Girls series.

One of my standard prompt structures for making images in Midjourney is this sequence of token modifiers:

[ medium ], [ subject ], [ pattern ], [ style ], [ params ]

I first describe a medium, such as water, a field of energy, or peanut butter.  This is followed by the primary subject of the image, which is usually a human, or maybe a robot or a dragon.  Then I apply a pattern, such as a texture ripples, fragmentation, or network connectivity.  The idea here is that the subject is between the medium and the pattern applied to the medium—therefore the subject becomes a combination of both. I then apply styles, such as 1980s vaporwave or 1920s cinema. Then the param are extra guidelines that influence quality, image size, and anything else that determines the final image output.

I may write another article that goes further into this prompt structure and process, but for now the point is that I often plug math into the [ pattern ] token modifier.

### The Math Formula

At the heart of this artistic process is a parametric math formula that brings life to the images being created. Let’s unravel its intricacies:

x(t) = A * cos(a * t) * cos(t) + A * sin(b * t) * cos(t)

y(t) = A * cos(a * t) * sin(t) + A * sin(b * t) * sin(t)

These equations can be analyzed as follows:

1. Both x(t) and y(t) are combinations of trigonometric functions (cosine and sine) of ‘t’ and linear combinations of ‘a’ and ‘b’ times ‘t’. These types of equations often describe oscillatory or periodic behavior.

2. The ‘A’ factor in both equations represents a scaling factor that determines the amplitude of the oscillations. The overall size of the curve will be proportional to the value of ‘A’.

3. The ‘a’ and ‘b’ factors in the equations determine the frequencies of the oscillations. By adjusting the values of ‘a’ and ‘b’, you can change the shape and complexity of the resulting curve. For example, if ‘a’ and ‘b’ are both integers, the resulting curve may exhibit a specific type of symmetry or periodicity.

4. The range of ‘t’ from 0 to 2π suggests that the curve is periodic and repeats its shape within this range. This can be further confirmed by analyzing the periodicity of the trigonometric functions.

The equations describe a parametric representation of a curve in two-dimensional space. A parametric representation means that both x and y coordinates are expressed as functions of a single parameter ‘t’, which ranges from 0 to 2π in this case. The constants ‘A’, ‘a’, and ‘b’ determine the specific shape, size, and orientation of the curve.

These curves are often known as Lissajous curves. Lissajous curves are the graphical representation of the motion of a point on a plane that is subject to two perpendicular periodic motions. These curve patterns can also be  known as harmonographs, which are known for their interesting and intricate patterns, depending on the chosen values for ‘a’ and ‘b’.

These parameters act as a guiding force, breathing dynamic motion into each stroke of the pixel brush on our digital canvas.

### Crafting Unique Expressions

With this mathematical foundation, we can embark on journies of infinite possibilities. By manipulating the variables within the formula, we unlock a vast array of expressive textures and mesmerizing patterns. Each combination of values breathes life into creations, resulting in a truly distinctive visual experience.

### Exploring Harmonious Curves

The presence of trigonometric functions, such as cosine and sine, within the formula plays a vital role in shaping the intricate curves and harmonious symmetries that define the images. Through careful influence of these functions, we can create fluid and captivating compositions that evoke emotions and ignite the imagination of viewers.

### Using the Power of Constants

The constants ‘A,’ ‘a,’ and ‘b’ provide individuality upon each piece. By adjusting their values, we can control the scale, amplitude, frequency, and complexity of the visual elements. This allows for the creation of a wide spectrum of moods, from serene and ethereal to vibrant and dynamic, all within the realm of a single formula.

### Beyond Numbers: Exercising Creativity

While mathematics provides the foundation, it’s the synergy between mathematical precision and artistic intuition that truly brings MidJourney prompting to life. In exploring the infinite possibilities offered by the formula, I exercise intuition, spontaneity, discernment in the liberating act of creative expression.

### Conclusion

In the realm of MidJourney prompts, the fusion of math and creativity becomes a way to discover and express unique visual experiences. By using  the influences of this math formula, we can weave intricate textures, captivating patterns, and expressions that stir the soul.