Creating the Geometry Nodes

Oct 13, 2025 by miodeya.com 43 views

Introduction

Geometry Nodes is a powerful tool in Blender that allows users to create complex 3D models and animations using a node-based system. In this article, we will explore how to use Geometry Nodes to select instances whose index# is a prime number. This is a unique and interesting problem that can be used to visualize prime numbers in a 3D environment.

Background

The Ulam Spiral is a famous mathematical concept that visualizes prime numbers in a 2D grid. The spiral starts at the center of the grid and moves outward in a spiral pattern, marking each prime number as it is encountered. By creating a 3D version of the Ulam Spiral, we can gain a deeper understanding of the distribution of prime numbers and their relationship to each other.

Using Python for Blender

Python for Blender is a powerful tool that allows users to write custom scripts and automate tasks in Blender. In this case, we will use Python for Blender to read a CSV file containing a list of prime numbers and use Geometry Nodes to visualize them in 3D.

Reading the CSV File

To start, we need to read the CSV file containing the list of prime numbers. We can do this using the csv module in Python. Here is an example of how to read the CSV file:

import csv

with open('prime_numbers.csv', 'r') as csvfile:
    reader = csv.reader(csvfile)
    prime_numbers = [int(row[0]) for row in reader]

This code opens the CSV file and reads it into a list of integers, where each integer represents a prime number.

Creating the Geometry Nodes

Now that we have the list of prime numbers, we can create the Geometry Nodes to visualize them in 3D. We will use a combination of nodes to create a 3D grid and then use a script to select the instances whose index# is a prime number.

Here is an example of how to create the Geometry Nodes:

import bpy
import mathutils

# Create a 3D grid
grid = bpy.data.objects.new('Grid', bpy.data.meshes.new('Grid'))

# Create a script to select the instances whose index# is a prime number
def select_prime_instances():
    # Get the list of prime numbers
    prime_numbers = [int(row[0]) for row in csv.reader(open('prime_numbers.csv', 'r'))]

    # Get the index# of each instance
    index_numbers = [i for i in range(len(prime_numbers))]

    # Select the instances whose index# is a prime number
    for i in index_numbers:
        if i in prime_numbers:
            grid.data.vertices[i].select = True

# Run the script
select_prime_instances()

This code creates a 3D grid and then uses a script to select the instances whose index# is a prime number. The script reads the CSV file containing the list of prime numbers and then uses a list comprehension to get the index# of each instance. Finally, it selects the instances whose index# is a prime number.

Visualizing the Prime Numbers

Now that we have selected the instances whose index# is a prime number, we can visualize them in 3D. We can use a combination of nodes to create a 3D visualization of the prime numbers.

Here is an example of how to visualize the prime numbers:

import bpy
import mathutils

# Create a 3D visualization of the prime numbers
visualization = bpy.data.objects.new('Visualization', bpy.data.meshes.new('Visualization'))

# Get the list of prime numbers
prime_numbers = [int(row[0]) for row in csv.reader(open('prime_numbers.csv', 'r'))]

# Get the index# of each instance
index_numbers = [i for i in range(len(prime_numbers))]

# Create a 3D grid to visualize the prime numbers
for i in index_numbers:
    if i in prime_numbers:
        # Create a cube to visualize the prime number
        cube = bpy.data.objects.new('Cube', bpy.data.meshes.new('Cube'))
        cube.location = mathutils.Vector((i, 0, 0))
        cube.scale = mathutils.Vector((1, 1, 1))
        cube.data.vertices[0].select = True
        visualization.data.vertices.append(cube.data.vertices[0])
        visualization.data.edges.append(cube.data.edges[0])

# Run the script
bpy.context.collection.objects.link(visualization)

This code creates a 3D visualization of the prime numbers by creating a cube for each prime number and then linking it to the visualization object.

Conclusion

In this article, we explored how to use Geometry Nodes to select instances whose index# is a prime number. We used Python for Blender to read a CSV file containing a list of prime numbers and then used Geometry Nodes to visualize them in 3D. We also created a 3D visualization of the prime numbers by creating a cube for each prime number and then linking it to the visualization object.

Future Work

There are many ways to extend this project. Some possible future work includes:

Creating a more complex 3D visualization of the prime numbers
Using a different algorithm to select the instances whose index# is a prime number
Creating a interactive visualization of the prime numbers
Using a different programming language to create the Geometry Nodes

References

Code

Introduction

In our previous article, we explored how to use Geometry Nodes to select instances whose index# is a prime number. We used Python for Blender to read a CSV file containing a list of prime numbers and then used Geometry Nodes to visualize them in 3D. In this article, we will answer some of the most frequently asked questions about this project.

Q: What is the Ulam Spiral?

A: The Ulam Spiral is a famous mathematical concept that visualizes prime numbers in a 2D grid. The spiral starts at the center of the grid and moves outward in a spiral pattern, marking each prime number as it is encountered.

Q: How do I create a 3D version of the Ulam Spiral?

A: To create a 3D version of the Ulam Spiral, you can use Geometry Nodes in Blender. You will need to create a 3D grid and then use a script to select the instances whose index# is a prime number.

Q: What is Geometry Nodes?

A: Geometry Nodes is a powerful tool in Blender that allows users to create complex 3D models and animations using a node-based system. It is similar to a flowchart, where each node represents a specific operation or function.

Q: How do I use Python for Blender?

A: Python for Blender is a powerful tool that allows users to write custom scripts and automate tasks in Blender. You can use it to read CSV files, create 3D models, and more.

Q: What is a CSV file?

A: A CSV file is a type of file that stores data in a table format, with each row representing a single record and each column representing a field. You can use a CSV file to store a list of prime numbers.

Q: How do I select the instances whose index# is a prime number?

A: To select the instances whose index# is a prime number, you can use a script to iterate over the list of prime numbers and select the instances whose index# matches the prime number.

Q: Can I use a different algorithm to select the instances whose index# is a prime number?

A: Yes, you can use a different algorithm to select the instances whose index# is a prime number. For example, you can use a sieve algorithm or a probabilistic primality test.

Q: Can I create a more complex 3D visualization of the prime numbers?

A: Yes, you can create a more complex 3D visualization of the prime numbers. For example, you can use a different shape or color to represent each prime number, or you can add additional features such as labels or animations.

Q: Can I use a different programming language to create the Geometry Nodes?

A: Yes, you can use a different programming language to create the Geometry Nodes. For example, you can use C++ or Java to create the Geometry Nodes, or you can use a scripting language such as Python or Lua.

Q: Where can I find more information about Geometry Nodes and Python for Blender?

A: You can find more information about Geometry Nodes and Python for Blender on the official Blender website, as well as on various online forums and communities.

Conclusion

In this article, we answered some of the most frequently asked questions about using Geometry Nodes to select instances whose index# is a prime number. We hope that this information is helpful to you, and we encourage you to explore the world of Geometry Nodes and Python for Blender further.

References

Code

The code used in this article is available on GitHub.