How to plot the Julia Set

In the previous post we discussed the Mandelbrot set. There is another beautiful algebraic fractal, called Julia set 𝓙. It is named after the French mathematician Gaston Julia, who has discovered. It is obtained by the same formula as the Mandelbrot Set: zn+1 = zn2 + c The difference is that z0 = x +Continue reading “How to plot the Julia Set”

Plotting the Mandelbrot Set

Calcpad has an interesting and undocumented feature, that I am going to reveal in this post. You can use it to quickly plot the Mandelbrot set. This is a set of complex numbers c, for which the iterative equation zn+1 = zn2 + c does not go to infinity. The most beautiful part is thatContinue reading “Plotting the Mandelbrot Set”

Even more 3D effects

In the last version I improved the 3D plot shading and added some nice 3D effects. Bellow is the plot of the function f(x; y) = cos(x) + cos(y) + cos(x·y/3)/2 + cos(√(x2 + y2)·2)/2 with the “Rainbow” color scale and the “Shadows” option on: What is new is the specular light effect (the littleContinue reading “Even more 3D effects”

Math Art with Calcpad

Most people consider math boring, but sometimes it can be really beautiful. Recently I found some unusual application of Calcpad – to draw nice pictures using math formulas. In general, you can plot functions of two variables using the $Map command: $Map{f(x;y) @ x = a : b & y = c : d} IContinue reading “Math Art with Calcpad”

Plotting with Calcpad 3.2

The new and enhanced version of Calcpad 3.2 was released. Besides other improvements, we added some nice visual effects for 2D plotting. In general, you can use Calcpad to plot functions of two parameters f(x; y), by the $Map command: $Map{f(x;y) @ x = a : b & y = c : d} The resultContinue reading “Plotting with Calcpad 3.2”