A much better fractal software package

1
A much better fractal software package

• Look at the two versions of the Snowflake Fractal
  Generator at http//www.shodor.org/master/fractal/
  software/

2
Finding the dimension

• Given your broccoli picture, determine how many
  of these measurements are needed to trace the
  curve as the crow flies.

3
Finding the dimension

• For each pair of rows, note that the scale factor
  is 1/2.
• Find the ratio of the number of copies (small
  measurement/large measurement).
• Use logs to solve the equation for dimension for
  each pair of rows.
• Ideally, your numbers should be close and
  converging to one value. However, many factors
  can alter this.

4
Building fractals from 2D

• Current method start with one-dimensional
  objects
• Alternate method start with two- dimensional
  objects
• Example Sierpinskis triangle and carpet
• Find the dimension of both objects.

5
Fractal Conclusions

• Fractals have dimensions between 1 and 2
• a dimension close to 1 means the fractal is more
  curve-like
• a dimension close to 2 means the fractal is more
  area-like

6
Fractal Conclusions

• Fractals are self-similar - portions of the
  fractal are copies of the whole figure.
• Fractals show the similar levels of complexity at
  all scales.