In this session, we’ll explore how complex functions can be harnessed — first through a mathematical lens, then through the lens of programming in R — to generate visually stunning and intricate patterns. By leveraging R’s capabilities, we demonstrate how concepts like symmetry, frequency, and phase can be translated into dynamic, animated visuals.
Key Mathematical & Theoretical Aspects:
- Complex Functions as Pattern Generators
- Understanding mappings and how real & imaginary parts interact to create geometry.
- Exploring transformations, rotations, and reflections emerging from complex operations.
- Symmetry, Frequency, and Phase
- Mathematical representation of symmetry in periodic and rotational systems.
- How frequency and phase modulation shape wave-based or iterative visual forms.
- Linking mathematical periodicity to visual repetition and motion.
- Iterative & Parametric Visualization
- Iterated transformations and their role in creating self-similar or fractal-like structures.
- Parametric curves and surfaces derived from complex expressions.
- Mathematics Meets Computation
- Translating analytic expressions into data for visual rendering.
- Numerical evaluation, discretization, and precision control in R.
R Programming Lens — Packages & Libraries We’ll Explore:
| Package / Library | Purpose & Role in the Talk |
| ----------------- | -------------------------- |
| tidyverse | Data manipulation, transformation, and visualization foundation. |
| ggplot2 + ggforce | High-level plotting tools for smooth geometric and parametric rendering. |
| gganimate | Animate mathematical transformations (phase shifts, rotations, iterations). |
| rgl / scatterplot3d | 3D visualization of complex mappings or parametric surfaces. |
| magick | Image manipulation and post-processing of frames. |
| gifski | Exporting smooth, high-quality GIF animations. |
| mathart (Marcus Volz) | A creative toolbox for mathematical art and generative geometry. |
| Rcpp | Accelerating computation for iterative or high-resolution mathematical data generation. |
What You’ll Take Away:
- A theoretical grasp of how complex-valued functions yield structured visual symmetries.
- Practical experience in implementing mathematical ideas using R’s visualization and animation tools.
- An understanding of how to use R as a medium for scientific art, blending computation, mathematics, and creativity.
- Inspiration to extend these concepts toward fractal generation, dynamic systems, and generative aesthetics.
