Math

The following are some p5js explorations about the beautiful and chaotic nature of mathematics. Feel free to explore these experiments and create your own verions of them. You can also see the code of some them and many more here.

Axis:
This is a simple example of a normal distribution. s a probability distribution that is symmetric and bell-shaped. It is characterized by its mean (μ) and standard deviation (σ). In a normal distribution, the majority of the data points cluster around the mean, with fewer data points further away from the mean.
Try it here.

Cardioid:
A mathematical cardioid is a geometric shape that resembles a heart. The cardioid is defined by the equation r = a(1 + cosθ), w-here- r is the distance from the origin to a point on the curve, θ is the angle measured from the positive x-axis, and a is a constant that determines the size of the cardioid. As θ varies from 0 to 2π, differentcurves that can resemble flowres, hearts and other shapes found in nature might appear.
Try it here.

Duffing Attractor: The Duffing attractor is a mathematical model that describes the behavior of a damped, driven oscillator. It is defined by differential equations. An attractor exhibits complex and chaotic behavior, with its trajectory forming intricate patterns in phase space. Try it here.

Lorenz Attractor: Perhaps the most famous attrator, The Lorenz attractor is a mathematical model that describes the behavior of a chaotic system known as the Lorenz system. It was first studied by Edward Lorenz in 1963 while investigating atmospheric convection, but it has since become a widely studied example of chaotic dynamics. It is also defined by non-linear differential equations. In this example you can rotate in 3D. Try it here.

Sprott: This attractor is a mathematical model that describes the behavior of a chaotic system. It was discovered by Tom Sprott and is defined by a set of non-linear differential equations. Try it here.

Logistic: The logistic map is a mathematical function that is commonly used in chaos theory and population dynamics. It is a recursive function that describes the behavior of a population over time. The logistic map is defined by the equation: x[n+1] = r * x[n] * (1 - x[n]) In this equation, x[n] represents the population at time step n, x[n+1] represents the population at the next time step, and r is a parameter that determines the growth rate of the population. Try it here.

Lissajou Curves: These figures, named after the French mathematician Jules Antoine Lissajous, are a type of parametric curve that describes complex harmonic motion. These curves are formed by the intersection of two perpendicular sinusoidal waves with different frequencies and phases. Try it here.