1. Holt Geometry 12-Ext Using Patterns to Generate Fractals 12-Ext Using Patterns to Generate Fractals Holt Geometry Lesson Presentation Lesson Presentation

2. Holt Geometry 12-Ext Using Patterns to Generate Fractals Describe iterative patterns that generate fractals. Objective

3. Holt Geometry 12-Ext Using Patterns to Generate Fractals self-similar iteration fractal Vocabulary

4. Holt Geometry 12-Ext Using Patterns to Generate Fractals A figure is self-similar if it can be divided into parts that are similar to the entire figure. You can draw self-similar figures by iteration, the repeated application of a rule.

5. Holt Geometry 12-Ext Using Patterns to Generate Fractals To create a self-similar tree, start with the figure shown in stage 0. Replace each of its branches with the original figure to get the figure in stage 1. Again replace the branches with the original figure to get the figure in stage 2. Continue the pattern to generate the tree.

6. Holt Geometry 12-Ext Using Patterns to Generate Fractals A figure that is generated by iteration is called a fractal.

7. Holt Geometry 12-Ext Using Patterns to Generate Fractals Example 1: Creating Fractals Continue the pattern to draw stages 3 and 4 of this fractal, which is called Cantor’s dust. To go from one stage to the next, remove the middle third from each remaining black line.

8. Holt Geometry 12-Ext Using Patterns to Generate Fractals Check It Out! Example 1 Explain how to go from one stage to the next to create the Koch snowflake fractal. Replace each line segment with the following figure.