Artmatic introduction

The controls
Here is the Artmatic screen. You will get used to the controls as you work.

Artmatic lets you create shapes as very sophisticated graphs. I hope you have learned that shapes corresponds to equations. The world has many shapes, but you have been taught equations for few of them. Artmatic gives you access to many more, and hence many more shapes. By manipulating the mathematical functions and their relationships you will manipulate shapes. Understanding the math is not necessary, but it is nice. This page hopes to let you see how the math works.

Implicit plotting
You are probably used the explicit form of an equation y = f(x), where y is solved as an explicit function of x and f(x) is one of only a few functions. This form of graphing is is very restrictive, and not very interesting, since functions have to pass the "vertical line test." As I love to say, "the heart is not a function." It is not a good way to create interesting shapes.

A better way is implicit plotting where both the x and the y are on the same side of the equation, for example the circle x² + y² = 1. Implicit plotting is more complex and more interesting. Many more shapes, and many more interesting shapes, can be created this way.

Artmatic as function plotter.

So lets get used to using this program to plot functions. By doing this you will make contact with the math that you know as well as learn how (in part) this program works.

Always begin simply. Choose the Basic option from the control that lets you choose the function tree.

When you choose this option you will see three boxes with flow lines that show how the numbers created by the functions are used. Hold down the mouse button over each box to choose the options shown in the picture. Each box option represents an implicit function or mathematical procedure.

Notice that these three boxes are different. The little green triangles at the top of each box are inputs; those at the bottom are outputs. The interior function (the top box) has two inputs and two outputs. It takes two numbers and gives two numbers. The middle function takes two numbers and gives one number. The bottom takes one number and gives one number.

First box: Each pixel has an x and a y coordinate. These coordinates are fed into the top two inputs on the top box, which takes the pixel coordinates and gives new x and y numbers using the mathematical procedure of that box. I usually set this first box to very simple functions. I call it the "basic processing box." The size and spacing of picture elements can usually be adjusted here.

The second box takes the new x and y values from the first box and, using its function, gives a single number, which will be used to look up the color. This is the implicit function and creates the shape of the graph.

The last box takes the color number and adjusts it. I set it to a simple setting and call this the final processing box. Usually the colors can be adjusted here.

This diagram describes the process.

Note: Artmatic can be very complicated and its effects are unpredictable. I always begin with something simple. I also always use the same simple initial and final boxes. When I create something more complicated it is in the middle boxes of the function tree structure.

Here is the picture created from the above setup.

Mixing pictures

Here is a simple tree setup that will create two pictures and them mix them together. This is not included in the default tree structures, you will have to create it yourself. Start with the "Basic" set, then add and subtract boxes to create this.

This accpts the x and y coordinates at the top but splits to create two pictures, one using the implicit functions sin x + sin y, and the other using the implicit function xy. The final control lets you set the final picture as a mixture of the two created pictures in which you can see the part created by the sine functions and the part created by xy.