Question

# Is it possible to create a random 2- dimensional shape using mathematical equations Or in software like 3D-max and AutoCAD?

Is it possible to create a random 2- dimensional shape using mathematical equations Or in software like 3D-max and AutoCAD? like this one:

## Top contributors to discussions in this field

Omid Vakili
University of Kurdistan
Yes, it is definitely possible to create a random 2-dimensional shape using mathematical equations or software like 3D Max and AutoCAD.
Using Mathematical Equations:
1. Parametric Equations: You can create a random shape by defining parametric equations that determine the x and y coordinates of points on the shape. For example, you could use sine and cosine functions with random parameters to create smooth curves, or use random step functions to create jagged shapes.
2. Random Point Generation: Generate random points within a defined boundary and then use interpolation or smoothing techniques to connect these points to form a shape.
3. Fractal Geometry: You can use fractal algorithms to generate intricate and complex shapes. For example, the Mandelbrot set is a famous example of a fractal shape.
Using 2D Software (e.g., 3D Max and AutoCAD):
1. Drawing Tools: Most 2D software packages provide various drawing tools that allow you to create shapes freehand, which you can then modify and transform to make them appear random.
2. Random Transformations: Apply random transformations like scaling, rotation, and translation to basic shapes like circles, squares, or polygons. Repeatedly applying random transformations can lead to more complex and organic shapes.
3. Noise Functions: Use noise functions to displace points on a shape, giving it a random and irregular appearance.
4. Procedural Texture Mapping: Create a texture that is procedurally generated using noise patterns or other algorithms, and then apply it to a simple shape. This can give the appearance of a complex and random pattern on the shape.
In both cases, the randomness can be controlled to various extents, allowing you to fine-tune the level of randomness or repeatability of the generated shapes.
Keep in mind that while the shapes may appear random, they are still generated by deterministic algorithms or equations. For truly unpredictable shapes, you might want to explore generative adversarial networks (GANs) or other advanced machine learning techniques, but that goes beyond the scope of traditional mathematical equations and standard 2D software.
2 Recommendations
Technische Universität Berlin
Dear Mr. Shabani,
Why not when there are more and more avenues available?
just as Mr. Omid stated using mathematical equations.
1 Recommendation
Kevin Barrera Llanga
Universitat Politècnica de Catalunya
Yes, it is feasible to create a random two-dimensional shape using specialized tools. If you are interested in finding a method to generate a similar shape randomly, I would recommend exploring innovative models like Stable Diffusion XL, which has been released recently. Using platforms like Google Colab, this model can be customized to craft a similar image, based on a clearly defined prompt. If the idea is to design a deep learning model, there is a variety of alternatives that can be explored, including but not limited to Generative Adversarial Networks (GAN), Variational Autoencoders, and other methods grounded in deep learning.
From my personal experience, I designed a model that operates in two stages and is based on GANs. In the initial stage, I approximate random numbers with the help of the Wasserstein metric, to approximate the distribution of random data (origin) to the distribution of peripheral blood cells, thus producing a low-resolution image. The second stage applies the generative concept of GAN in an image-to-image approach. This approach enables me to bring the data distribution closer between one image and another, thereby improving its quality. To achieve this, I make use of the Pix2Pix technique, which allows a precise conversion of the characteristics of one image into another, maintaining some attributes while altering others. If you are intrigued to know more about this project, I invite you to read the publication where I detail the work carried out:
1 Recommendation

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