From 23712d26436fd1b56c1a50eecf15272128cc9b35 Mon Sep 17 00:00:00 2001 From: JP Appel Date: Mon, 6 May 2024 18:07:07 -0400 Subject: complex fractals structure --- static/projects/complex-fractals/presentation.html | 410 +++++++++++++++++++++ 1 file changed, 410 insertions(+) create mode 100644 static/projects/complex-fractals/presentation.html (limited to 'static/projects/complex-fractals/presentation.html') diff --git a/static/projects/complex-fractals/presentation.html b/static/projects/complex-fractals/presentation.html new file mode 100644 index 0000000..3cb9e88 --- /dev/null +++ b/static/projects/complex-fractals/presentation.html @@ -0,0 +1,410 @@ + + + + + + + + HPC Complex Fractal Generation + + + + + + + + + +
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HPC Complex Fractal Generation

+

JP Appel

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+ +
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+

Prerequisite Knowledge

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+

Complex Numbers

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i2 =  − 1 z = x + iy

+ +
+

Addition

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z1 + z2 = (x1+x2) + i(y1+y2)

+ +

Multiplication

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z1z2 = (x1x2−y1y2) + i(x1y2+x2y1)

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+

What is the Mandelbrot Set

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+

zn = zn − 12 + z0

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Fractals

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    +
  • infinite self-similar geometric shape
    • +
  • have “fractional dimension”
    • +
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+Sripenski Triangle + +
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+

The Mandelbrot set is a fractal in the complex plane

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Fractal in Nature

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+Romanesco Cauliflower + +
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+

Escape Time Algorithm

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    +
  • Inputs +
      +
    • Maximum Number of iterations
      • +
    • Upper bound
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    • +
+
    +
  1. Create a grid of points to sample
    2. +
  2. For each point in the sample space +
      +
    1. Compute the next term in the sequence
      2. +
    2. if greater than the upper bound return the number +of iterations
      3. +
    3. else repeat until the maximum number of iterations +and return
      4. +
    3. +
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Implementation

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Program Structure

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Mandelbrot

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Image

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Tricorn

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Image

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Burning Ship

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Image

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Multibrot

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Image

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Multicorn

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GIF

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Julia

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Image

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Analysis

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Interactive Plots

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+ + + + + + + + + + + -- cgit v1.2.3