Blog Formatting Guide

This post demonstrates all the formatting options available for PySimHub blog posts.

Text Formatting

You can write bold text, italic text, and bold italic text. You can also use inline code for technical terms or short code snippets.

Blockquotes are great for highlighting important information or quoting sources. They stand out with an accent-colored left border.

Here’s a link to the PySimHub homepage and an external link to GitHub.

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Headings

The heading above is an H2. Below are examples of other heading levels:

This is an H3 Heading

This is an H4 Heading

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Lists

Unordered Lists

• First item
• Second item
  • Nested item
  • Another nested item
• Third item

Ordered Lists

1. First step
2. Second step
3. Third step
   1. Sub-step A
   2. Sub-step B

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Code Blocks

Inline code looks like this. For longer code, use fenced code blocks:

import numpy as np
from scipy.integrate import odeint

def lorenz(state, t, sigma=10, rho=28, beta=8/3):
    """The Lorenz system of differential equations."""
    x, y, z = state
    return [
        sigma * (y - x),
        x * (rho - z) - y,
        x * y - beta * z
    ]

# Initial conditions and time span
initial_state = [1.0, 1.0, 1.0]
t = np.linspace(0, 50, 10000)

# Solve the system
solution = odeint(lorenz, initial_state, t)

// JavaScript example
const simulate = async (model, params) => {
  const results = await model.run(params);
  return results.map(r => r.value);
};

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Mathematics

PySimHub blog posts support LaTeX math rendering via KaTeX.

Inline Math

The famous equation shows the equivalence of mass and energy. The Reynolds number characterizes flow regimes.

Display Math

The Gaussian integral:

A simple differential equation solution:

Summation example:

Matrix notation:

The Navier-Stokes equations:

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Tables

Method	Accuracy	Speed	Use Case
Euler	Low	Fast	Quick estimates
RK4	High	Medium	General purpose
Adams-Bashforth	High	Fast	Long simulations
Implicit	Very High	Slow	Stiff systems

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Images

Standard markdown images:

For more control, use HTML figure elements:

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Combining Elements

Here’s an example combining text, math, and code to explain a concept:

The Euler method is the simplest numerical integration technique. Given an ODE , we approximate the solution at discrete time steps:

where h is the step size. Implementation in Python:

def euler_step(f, t, y, h):
    """Perform one Euler integration step."""
    return y + h * f(t, y)

Note: While simple, the Euler method has local error, making it less accurate than higher-order methods like RK4.

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Summary

This guide covered:

1. Text formatting - bold, italic, links, blockquotes
2. Structure - headings, lists, horizontal rules
3. Code - inline and fenced code blocks
4. Math - inline and display LaTeX equations via the Math component
5. Media - images and figures with captions
6. Data - tables for structured information

Happy writing!