Name: Creating Dynamic Patterns with Complex Functions in R
Start: 2025-11-16T19:00:00+05:30
End: 2025-11-16T20:30:00+05:30

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:**

1. **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.

2. **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.

3. **Iterative & Parametric Visualization**

* Iterated transformations and their role in creating self-similar or fractal-like structures.
* Parametric curves and surfaces derived from complex expressions.

4. **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**.

Samrit Pramanik

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Abhirup Moitra, a researcher, educator, and science communicator with a strong foundation in mathematics and statistics. As a **young scholar with deep intellectual curiosity** and **strong analytical and computational skills**, Abhirup has engaged in rigorous mathematical research while maintaining a commitment to clarity and accessibility. His work often integrates **rigors mathematics** with **data visualization and simulation**, helping to make abstract ideas more intuitive and visually engaging for learners and enthusiasts alike.
Beyond research, Abhirup is a **founding member of Cosmic Charade**, a science communication platform, and an **assistant organizer of the Kolkata R User Group**, where he coordinate events and instruct for scientific computing. As science and technology continue to evolve rapidly in this ever-advancing technological era, **Abhirup Moitra** remains committed to bridging the gap between rigorous theory and practical understanding. Through his active engagement in **research collaborations, teaching, and science communication**, he aims to **advance the frontiers of pure mathematics and computational sciences**, while **fostering broader public appreciation and accessibility** of these complex ideas.

Abhirup Moitra

Creating Dynamic Patterns with Complex Functions in R

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Creating Dynamic Patterns with Complex Functions in R

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