From 3efffb9ca98303487cf091447c7ba3fba3c71df8 Mon Sep 17 00:00:00 2001 From: JP Appel Date: Tue, 30 Apr 2024 06:46:31 -0400 Subject: finishing changes to presentation --- presentation/presentation.html | 411 +++++++++++++++++++++++++++++++++++++++++ presentation/presentation.md | 15 +- 2 files changed, 422 insertions(+), 4 deletions(-) create mode 100644 presentation/presentation.html (limited to 'presentation') diff --git a/presentation/presentation.html b/presentation/presentation.html new file mode 100644 index 0000000..31c1443 --- /dev/null +++ b/presentation/presentation.html @@ -0,0 +1,411 @@ + + + + + + + + HPC Complex Fractal Generation + + + + + + + + + +
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HPC Complex Fractal Generation

+

JP Appel

+

David Marrero

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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

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+

Addition

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z1 + z2 = (x1+x2) + i(y1+y2)

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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
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    • Upper bound
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    • +
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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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+ + + + + + + + + + + diff --git a/presentation/presentation.md b/presentation/presentation.md index b3297c3..a4a1f4f 100644 --- a/presentation/presentation.md +++ b/presentation/presentation.md @@ -139,6 +139,8 @@ The Mandelbrot set is a fractal in the complex plane ## Mandelbrot +[Image](../examples/mandelbrot.png) + ::: notes * when mandelbrot initially tried to have this printed, the printers kept removing the "dust" thinking it was an error in their printing process @@ -147,19 +149,24 @@ The Mandelbrot set is a fractal in the complex plane ## Tricorn +[Image](../examples/tricorn.png) + ## Burning Ship +[Image](../examples/burning_ship.png) + ## Multibrot +[Image](../examples/multibrot.png) + ## Multicorn -## Julia +[GIF](../examples/multicorn.gif) -## Serial Animation -## Shared Animation +## Julia -## CUDA Animation +[Image](../examples/julia.png) # Analysis -- cgit v1.2.3