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I Built a Finite-Element Solver With Nothing to Hide
A transparent, dependency-free capacitor simulator — and an honest account of exactly where a simple mesh lets it down. Every physics course teaches the parallel-plate capacitor formula in the first week: Clean. Memorable. Wrong the moment your capacitor isn't two infinite plates in a... -
A Measured Formulation of the Shadow View of Collatz
A different way to look at one of mathematics’ most stubborn problem A useful way to think about the Collatz map is to separate the orbit into two layers: the parity pattern of the terms and the arithmetic values that carry that pattern. The Accelerated Collatz Formulation This perspective... -
A Triplet-Based Parameterization for the Local Asymptotic Characterization of Polynomial Roots
Abstract This paper introduces a compact three-parameter framework for characterizing the local geometry of polynomial roots. DOI (Zenodo) For each root, the framework records its position, its algebraic multiplicity, and a newly defined quantity called the characteristic deflection distance... -
Python QuTiP Quantum Toolbox in Python
QuTiP is open-source software for simulating the dynamics of open quantum systems. The QuTiP library depends on the excellent Numpy, Scipy, and Cython numerical packages. In addition, graphical output is provided by Matplotlib. QuTiP aims to provide user-friendly and efficient numerical... -
Python Collection of Python Projects (The Beauty of Mathematics)
GitHub Repository The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics." – G. H. Hardy (1877–1947) -
The Universe Never Forgets — It Just Grows
The Universe Never Forgets — It Just Grows A Mathematical Thought Experiment at the Edge of Physics Check out the full proposal and Python simulation at The Golomb Universe ⌛ The “Quantum Memory Paradox” At the smallest scales, quantum mechanics demands that information is preserved — a...- ratwolf
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The Fractal Heart of Weierstrass
I experimented a bit with the famous, or rather infamous, Weierstrass function. The result was something like a Weierstrass toolkit, which allows you to represent the function, extended two-dimensionally, as a fractal (value probability density view) and more. I don't know if or who is...- ratwolf
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How Stereographic Projection Reveals an Emergent Dimension
GitHub The stereographic projection offers a fascinating analogy for understanding emergent dimensions — the idea that higher-dimensional information can be encoded in a lower-dimensional surface. While not a direct physical model, it helps visualize how the third dimension of spacetime might...- ratwolf
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Python Wallpaper for the mind, a forgotten old classic
Wallpaper for the mind, a forgotten old classic -
Wallpaper for the mind, a forgotten old classic
import numpy as np import matplotlib.pyplot as plt # Constants WIDTH, HEIGHT = 400, 400 # Grid resolution CORNER_A = -15 # Lower-left corner CORNER_B = -25 # Lower-right corner SIDE = 41 # Side length of the square grid NUM_COLORS = 4 # Number of distinct colors def...- ratwolf
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Python 3D Rotation using Quaternions
3D Rotation using Quaternions -
3D Rotation using Quaternions
import numpy as np import matplotlib.pyplot as plt from matplotlib.animation import FuncAnimation import quaternion # Requires 'numpy-quaternion' package def setup_figure(): fig = plt.figure(figsize=(10, 8), dpi=100) ax = fig.add_subplot(111, projection='3d') lim = (-1.5, 1.5)...- ratwolf
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"Less is More: Your Best Python One-Liner?"
Estimate π via the Monte Carlo method: import numpy as np; print(4 * np.mean(np.sum(np.random.rand(10**7, 2)**2, axis=1) < 1))- ratwolf
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Python Generate a Secure Random Password in One Line!"
Want to generate a secure, random password in just one line of Python? Here's a quick one-liner using random and string modules: import random, string password = ''.join(random.choices(string.ascii_letters + string.digits + string.punctuation, k=12)) print(password) This creates a random... -
Fractal design with Golomb rulers
You really have to ask yourself who comes up with such ideas:eek: GitHub - ratwolfzero/Golomb: Fractal design with Golomb rulers- ratwolf
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Do you want to travel far away this weekend?
Why don’t you take Alcubierre's warp drive! Warp Drive in a Nutshell The concept of a warp drive—a theoretical propulsion system that allows faster-than-light travel—was first mathematically formalized by physicist Miguel Alcubierre in 1994. Inspired by the idea of bending space-time, Alcubierre...- ratwolf
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- Forum: General Discussion
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Can You Identify the Unsolved Mathematical Problem?
Below is a Python program that implements a simple yet unsolved mathematical problem. A validation result is displayed in the plot title. Your Task: Run the code and observe the output or analytically follow the code's logic. Identify the mathematical problem being implemented. Explain why...- ratwolf
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- Replies: 2
- Forum: General Discussion
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Python The Secret of Nim (visual/layout improvements welcome)
The Game of Nim and the mathematical background of how to win the game GitHub import numpy as np import matplotlib.pyplot as plt from matplotlib.widgets import Slider # Constants SAFE_COLOR = "seagreen" # Green for safe positions UNSAFE_COLOR = "tomato" # Red for unsafe positions... -
Update! Weekend Challenge: Still no idea what to do on the weekend?
Below a fixed example for a 3D sphere Challenge: Design and implement an algorithm that takes as input a smooth, parametrically defined 3D surface described by analytic formulas. This algorithm should automatically determine a suitable projection center for stereographic projection and compute...- ratwolf
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