Wonder and the Mandelbrot set

There’s something about wonder that Mandelbrot fans may have noticed.  The shape of wonder and much of the imagery in wonder is based on fractal patterns that can be found in the Mandelbrot Set.  The Mandelbrot set is a mathematical wonder named after Benoit Mandelbrot for his discovery of fractal geometry and work on the set.   

The Mandelbrot set exists only in mathematics.  It’s drawn on the complex plane, where real and imaginary numbers meet, using a very simple equation.  When you zoom in on the edge of the Mandelbrot set, endless intricate fractal patters appear.  It even contains miniature copies of itself.  

Here’s a zoom sequence of the Mandelbrot set from Mathigon on YouTube showing the intricate details that emerge when you zoom in on the edge of the Mandelbrot set.  It starts with a view of the outline of the Mandelbrot set and then continuously zooms in:

The Quotes in Wonder

Have you ever wondered what wonder is?  How, from within ourselves, we can wonder about the world outside?  Benoit Mandelbrot and Stephen Wolfram opened new ways to think about these questions.  The quotes are from videos of these great wonderers sharing what they found.    

Benoit Mandelbrot Quote

Benoit Mandelbrot discovered and developed the field of fractal geometry, creating an entirely new mathematical understanding of the shapes of nature.  The video below is from a 2010, TED talk Mandelbrot gave titled, “Fractals and the art of roughness”, where he shares thoughts about his life, work and fractals.  The quote, “Bottomless wonders spring from simple rules, which are repeated without end”, appears at the end of the video.   

Here’s Mandelbrot’s Ted Talk on YouTube:

Stephen Wolfram Quote

Stephen Wolfram’s work on the computation and the computational universe has created a new kind of science, which is also the title of a book he published in 2002.  The quote, “…how does an entity embedded in the ruliad perceive the ruliad?”, is from a presentation Wolfram gave at titled, “Making Everything Computational- Including the Universe” at the 2022 Information Universe conference.  The quote is an excerpt, the complete quote is,  “We are entities embedded within this ruliad, so we have to ask the question, how does an entity embedded within the ruliad perceive the ruliad.” Wolfram describes the ruliad as, “…the entangled limit of following all computational rules”.The quote can be found at around 35:57 in the video, and it’s part of an even larger concept, the computational universe.

Wolfram’s work is profound and far reaching, and best heard in their entirety in Wolfram’s own precise words.  

Here’s Wolfram’s presentation on YouTube: