IFS Function

The images you see to the right were all created with IFS Function.*

IFS Function Logo

Click here or click the logo above for a test drive!

What is IFS Function?

How do you use IFS Function?

What are .uifs files?

IFS Function is free software. Download it at Sourceforge!
© 2007 Leon Q. Brin

* The x and y values shown give the coordinates of the yellow highlighted point on the graph.






What is IFS Function?

IFS Linear is a program for creating affine fractal interpolation functions.  Though you don't need to know it in order to use the program, the functions it produces are actually iterated function system (IFS) fractals.  That's where it gets the "IFS" part of its name. 

How do you use IFS Function?

  1. Basic Usage
    1. The Design Area
    2. Other Features
  2. Tips
    1. Parabolas
    2. What are the plus signs for?

1. Basic usage

a. The Design Area

When the applet starts up, you should see a gridded design area. That grid is where you will design your function. This diagram shows the various parts of the design area.

IFS Function Design Area
  • Data Points: These are the data points through which the interpolating function must pass. They may be clicked and dragged around. A data point may be deleted by clicking the Delete Tool (delete tool) next to it. Notice data points appear at the corners of scaling tabs.
  • Insert Data Point Tools: Click these in order to add data points to the function. The maximum number of data points for any given function is 10. Notice they appear at the midpoints of the sides of the scaling tabs.
  • Scaling Tab: Click and drag this tab to increase or reduce the scaling factor of the corresponding segment of the function. This increases or decreases the fractal dimension of the interpolating function.
  • x-value Marker: Click and drag this point left and right to change the x-value of the highlighted point in the preview area.

b. Other Features

Clicking the "Restart" button returns the default starting parabola to the design area.

Clicking "Snap to Grid" makes mouse dragging motions "snap" from one location to another. With "snap" on, the tools can only be placed in limited locations. This is useful, for example, if you want to place data points exactly on grid crossings or half-way points. Notice that when you click the button, it turns into a "Freehand" button. Clicking the "Freehand" button removes "snapping."

When you want a closer look at what you see in the preview area, you might want to click on the "Render Fractal" button. This will bring up a dialog box that allows you to create a larger, more colorful version of your interpolating function. This is more useful for some of the other IFS Tools, but you may find it interesting to try here as well.

2. Tips

a. Parabolas

When IFS Function starts up, the interpolating function you see is actually a parabola. Not just a good imitation, but a legitimate parabola. It is the parabola satisfying the equation

p(x) = -2x(x-1)

If you click and drag any of the data points vertically, the interpolating function remains a parabola. Different parabolas for different configurations of data points, of course, but parabolas nonetheless.

b. What are the plus signs for?

Each segment (interval between two consecutive data points) of the interpolating function is an exact replica, scaled and sheared, of the entire interpolating function. For a segment with a plus sign, the copy has the same left-to-right orientation as the whole funtion. For a segment with a minus sign, the copy has the opposite (right-to-left) orientation.

What are .uifs files?

The .uifs files hold the coordinates of the data points, whether each segment should be replicated forward or backward, and the scaling factor for each segment. In other words, they store the mathematical description of the interpolating function.

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