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    Amir Asghari | Interactive Apps

    Welcome to my portfolio of interactive projects. Below is a collection of web applications I’ve designed for teaching and exploring concepts in mathematics.

    Arithmetics and Algebra

    Multiplication Web

    A game to build an understanding of multiplication by unlocking facts using strategies like the distributive property.

    Multiplicative Sums

    An interactive color pad for exploring the multiplicative structure of numbers, particularly the sums of the first N powers.

    Fractals and Chaos

    Cantor Set Explorer

    Generate stages of the Cantor set, explore its properties with zoom and pan, and calculate its box-counting dimension.

    Crumpled Paper Dimension

    An interactive lab to analyze the fractal dimension of a crumpled ball by plotting its mass vs. radius on a log-log scale.

    Koch Snowflake Explorer

    Construct the classic Koch snowflake, explore its infinite perimeter, and analyze its fractal dimension using a box-counting lab.

    Logistic Map Explorer

    Visualize the behavior of the logistic map through its bifurcation diagram and orbit plots. Estimate the fractal dimension of its strange attractor.

    Sierpiński Triangle Explorer

    Construct the Sierpiński triangle recursively. Includes interactive zoom/pan and a lab for calculating the box-counting dimension.

    Numerical Integration

    Numerical Integration Lab

    Visually compare the Midpoint, Trapezoidal, and Simpson’s rules for approximating integrals and analyze their error rates.

    Romberg Integration Lab

    Explore the powerful Romberg method, which uses Richardson extrapolation to achieve high accuracy with fewer steps.

    Numerical Methods

    Decimal Search Root-Finder

    An interactive lab for finding the roots of equations using the Bisection Method, also known as interval or decimal searching.

    Fixed-Point Iteration Visualizer

    Visualize how the fixed-point iteration method finds roots, and see why some functions converge while others diverge.

    Linear Interpolation Root-Finder

    Finds roots of equations using the Method of False Position. Visualize how it uses a secant line to make intelligent guesses.

    Root-Finding Method Comparison

    A dashboard to visually compare the performance of five different root-finding algorithms on the same function.

    Secant & Newton-Raphson Methods

    Visually compare two advanced root-finding algorithms. Explore their speed and convergence on user-defined functions.

    Taylor Series Visualizer

    Explore how functions are approximated by polynomials. Visually compare a function to its Taylor series and analyze the error.

    Solution of Ordinary Differential Equations

    ODE Solver & Error Comparison

    Compare the long-term accuracy and error accumulation of various methods for solving ordinary differential equations.

    ODE Step Visualizer

    Visually explore the geometry of a single step for the Euler, Modified Euler, and Runge-Kutta (RK4) methods.

    Taylor Method for ODEs

    Explore how using higher-order derivatives in a Taylor series creates highly accurate solutions for differential equations.