Thursday: Review last lab: lab 8.
New lab: lab 9 Recursion.
Modifying Images:
- Brightening: increase the value of each RGB component.
- Threshold: For each RGB component: if (rgb value < threshold), set value to zero, otherwise set to 256
- Posterize: Similar to Threshold except that there are intermediate thresholds (e.g. val<32, set to 0; val < 64, set to 32; etc
- Invert component: replace val with 256-val.
- Impressionist: randomly replace pixels with dots of some radius.
- Grayscale: replace each component with average of three rgb components.
- Convolution: Edges (e.g. see Sobel Edge Detector), blurring, sharpening
Generating Images using Recursion
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Turtle Graphics
Also see examples at fractals: Sierpinski Triangle, Koch Snowflake, Self-Similarity. Cellular Automatons
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Fractals
- Willamette Math Emeritus Faculty: Junpei Sekino's Fractal page.
- Complex Numbers:
- Defined: Wikipedia, Dave's short course, many other web references are also available.
- Applications
- Question Corner: electric circuits, electromagnatism.
- Wikipedia
- Equations:
- Mandelbrot set: For each point C in the complex plane, iterate: z(t+1) = z2(t) + C, where z(0) = 0
- Julia set: Fix a value of C. For each point W in the complex plane, iterate: z(t+1) = z2(t) + C, where z(0) = W
- Fractal generator and Jackson Pollack painting
- Fractal Mountains: Example 1 and Example 2.
- Fractal Dimension
Povray and Iteration:
- Lorentz attractor
and
povray code: lorenz.pov
Povray and Recursion:
- 1D Koch Diagram.
and
povray code: koch1D.pov
- See Julia Fractal in Povray online help.
- Fractal Examples generated using Povray.
- 3D Sierpinski Triangle
and
povray code: sierpinski.pov
- 3D Sierpinsky's carpet.
and
povray code: carpet.pov
- Recursive tree:
and
povray code: tree.pov
