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low cost private java apache 0; } } public void paint(Graphics g) { double x1,y1,x2,y2; int i, j1, j2; j1 = yvalue(0); for (i = 0; i < AppletWidth; i++) { j2 = yvalue(i+1); g.drawLine(i, j1 ,i+1, j2); j1 = j2; } } private int yvalue(int ivalue) { // Given the xpoint we're given calculate the Cartesian equivalent double x, y; int jvalue; x = (ivalue * (xmax - xmin)/(AppletWidth - 1)) + xmin; // Take the sine of that x y = Math.sin(x); // Scale y into window coordinates jvalue = (int) ((y - ymin)*(AppletHeight - 1)/(ymax - ymin)); // Switch jvalue from cartesian coordinates to computer graphics coordinates jvalue = AppletHeight - jvalue; return jvalue; } } Now we can adjust the range over which we graph without modifying our code!So far we've only graphed sine functions. It should be obvious how to modify the code to graph cosines or many other kinds of functions. However what if we want to define the function at runtime? Exercises Add labeled coordinate axes to the graph.
low cost private java apache Our graph method handled mathematical functions. How would you need to change it and what features would you add to make it suitable for plotting discrete experimental data? An infinite set that with zero lengthWe're now going to use Java to implement some classic examples of fractal geometry. We'll do three of these. We begin with a one-dimensional set with an infinite number of points that covers zero length. Then we'll investigate the Koch snowflake.
low cost private java apache Finally in the next chapter we'll delve into the most famous fractal of all, the Mandelbrot set.The middle third set is defined by starting with all the real numbers between zero and one inclusive. Then we cut out the middle third of that set (exclusive of the endpoints). i.e.
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