It appears as though I was looking into how the Fibonacci sequence could be made continuous, thinking about the rate of change of the sequence, etc.

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fibonacciSequence.java

public class fibonacciSequence {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// First, we generate the series. Then, we divide each term by the sum of all previous terms. 
		//The resultant list is below, it approaches a value then diverges. Note that once it diverges, 
		//the new value is the Fibonnaci sequence. 

		double sequence[] = new double[100];
		sequence[0] = 0;
		sequence[1] = 1;
		int sum=0;
		for (int i = 2; i < 100; i++) {
			sequence[i] = sequence[i - 1] + sequence[i - 2];
			
		}

		for (int i = 2; i < 100; i++) {
			sum=0;
			for(int k=0;k<i;k++){
				sum+=sequence[k];
				}
			System.out.println(i+"       "+sequence[i]/sum);
			
		}
	}
}
//How can we make the Fibonacci sequence continuous? Can we add many of the same series each of which 
//has a second term that is slightly larger than the first? Say one series is: 0,.01,.01,.02,.03 etc. 
//Another being: 0,.02,.02,.04 etc.
//I'm not sure if the above method would work...I'm trying to think of a way I can make a series continuous. 

//What's the rate of change of the Fibonacci sequence? I think it may be something like F'(n)=F(n-1).
//This is an interesting property.

fibonacciSequenceMethods.java

import java.awt.*;
import javax.swing.*;
public class fibonacciSequenceMethods {

	/**
	 * I've realized what I can do. After briefly reading something about the fibonacci sequence and how it relates to the golden ratio I'm going to graph an inverse fibonacci sequence. 
	 * This can be a spiral or anything else. I don't like the idea of replicated something else, such as the spiral. I'd prefer to do something original. I'll cease my researching (which was 
	 * transient and unintentional; I wasn't looking for ideas) and continue on my own. Hopefully I'll still have the motive once I finish whatever work is required of me on this school day. 
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		JFrame Fibonacci = new JFrame("Visual Fibonacci");
		/** Create a JFrame 
		 */
		Fibonacci.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
		/** Make the program exit when the frame is closed
		 */
		JLabel textLabel = new JLabel();
		/** Create a new label
		 */
		textLabel.setText("I'm A Label");
		/** Add text to the label, images can also be added
		 */
		textLabel.setSize(300, 100);
		/** Size the label
		 */
		Fibonacci.getContentPane().add(textLabel);
		/** Add the label to the frame
		 */
		Fibonacci.pack();
		/** Sizes the frame so it fits all of it's components nicely
		 */
		Fibonacci.setVisible(true);
		/** Show the frame
		 */
		textLabel.setVisible(true);
		/** Show the label
		 */	
	}	
}