We will gather and analyze fractal images from various Internet sources. We will determine whether the selected patterns of pictures obtained are indeed fractals and if so, the fractal dimensional value for each.
We will utilize Netscape to search for Internet Sources of fractals, down load the images in a JEPG or JIFF format (so that they can be saved to disc) and also print them out as black and white images.
The images will then be scanned and converted into PICT forms using the software program capture or by simultaneously typing command (apple key), shift, & (#3). The software programs, Mac Paint or the NIH will then be used to "clean up" the images, removing "fractal noise particles".
They will then be analyzed with the software program Fractional Dimension 6.0a1.02 utilizing the box and circle methods. The graphs obtained will then be saved as PICT files, printed out and will be analyzed and discussed.
Please refer to graphs, "Pictures and Graphs." (Coming Soon).
| Box Method Fractal Dimension | Cirlce Method Fractal Dimension | |
|---|---|---|
| Drum Head Fractal | 1.787 | 1.865 |
| Retinal Neuron Fractal | 1.418 | 1.321 |
| Snowflake Fractal | 1.742 | 1.865 |
Note that all of the slopes of all of the lines have non-integer values.
As all of the slope values are non-integers, we concluded that these images are all indeed fractals. In all cases, the fractal dimension values were relatively close to each other.
This activity provides students with the opportunity not only to study fractals but also to use technology to study and analyze them. This interdisciplinary activity would be suitable for any computer, mathematics or science course at the middle school or high school level. As an extension of the project, we will require students to identify, gather and analyze biological and physical examples of fractal patterns in order to determine the fractal dimensional values. We suggest that this activity can occur near the beginning of the school year and be integrated as a part of a unit, interrelating the disciplines of language arts, mathematics, science and technology. For example, this activity could be the first unit on data collection and analysis, construction of graphs and reintroduction of the concept of slope.