EBK BUILDING JAVA PROGRAMS
EBK BUILDING JAVA PROGRAMS
4th Edition
ISBN: 9780134323718
Author: Stepp
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 12, Problem 16E
Program Plan Intro

Sierpinski carpet program

Program plan:

  • Import the required packages.
  • Create the class “SierpinskiCarpet”.
    • Define the “size” to “243”
    • Define the “main()” method.
      • Create an object for scanner class.
      • Get the value from the user.
      • Initialize drawing panel.
      • Create an object for graphics.
      • Call the method “drawBox()”.
    • Define the method “drawBox()”.
      • Check whether the “stage” is greater than “0”.
        • Get the size.
        • Call the method “fillRect” to fill the size.
        • Traverse the “for” loop to refer the row.
          • Traverse the “for” loop to refer the column.
            • Call the method “drawBox()” recursively.

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Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…
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The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…
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