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.

#### 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;
sequence = 0;
sequence = 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
*/
/** 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
*/
}
}
```
```