A fractal landscape is a surface that is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain. In other words, the result of the procedure is not a deterministic fractal surface, but rather a random surface that exhibits fractal behavior. Many natural phenomena exhibit some form of statistical self-similarity that can be modeled by fractal surfaces. Moreover, variations in surface texture provide important visual cues to the orientation and slopes of surfaces, and the use of almost self-similar fractal patterns can help create natural looking visual effects.The modeling of the Earth's rough surfaces via fractional Brownian motion was first proposed by Benoit Mandelbrot. Because the intended result of the process is to produce a landscape, rather than a mathematical function, processes are frequently applied to such landscapes that may affect the stationarity and even the overall fractal behavior of such a surface, in the interests of producing a more convincing landscape. According to R. R. Shearer, the generation of natural looking surfaces and landscapes was a major turning point in art history, where the distinction between geometric, computer generated images and natural, man made art became blurred. The first use of a fractal-generated landscape in a film was in 1982 for the movie Star Trek II: The Wrath of Khan.Loren Carpenter refined the techniques of Mandelbrot to create an alien landscape. (Wikipedia).
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From playlist research
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
Fractals are typically not self-similar
An explanation of fractal dimension. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/fractals-thanks And by Affirm: https://www.affirm.com/careers H
From playlist Explainers
What are fractals? Just look at your broccoli to find out! License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Measurement
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/8wEX
From playlist 3D printing
The Beauty of Fractal Geometry (#SoME2)
0:00 — Sierpiński carpet 0:18 — Pythagoras tree 0:37 — Pythagoras tree 2 0:50 — Unnamed fractal circles 1:12 — Dragon Curve 1:30 — Barnsley fern 1:44 — Question for you! 2:05 — Koch snowflake 2:26 — Sierpiński triangle 2:47 — Cantor set 3:03 — Hilbert curve 3:22 — Unnamed fractal squares 3
From playlist Summer of Math Exposition 2 videos
From forests to farms and skies to shores, we’re surrounded by fractals. These infinitely complex patterns, which emerge from repeating a simple process over and over, are aesthetically astonishing and a valuable tool for creating meaning from chaos. Tonight, practice your pattern recognit
From playlist After Dark Online | Thursday Nights | Exploratorium
Painting a Landscape with Maths
Today we are painting a landscape using mathematics. Support this channel: https://www.patreon.com/inigoquilez Buy this painting in a metal, canvas or photographic paper print: https://www.redbubble.com/shop/ap/39843511 This is the link to the real-time rendering code (that you can edit y
From playlist Painting with Maths
Benoit Mandelbrot - Fractals and the art of roughness [HD] [2010]
Fractals and the art of roughness Benoit Mandelbrot At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated. h
From playlist Mathematics
Delicia Kamins - Philosophy of Fractals - CoM Oct 2020
We know that fractals are nature’s pattern makers. Fractals are in fact everywhere we look: tree bark, snowflakes, mountain ranges, cloud, rivers, seashells, all the way up to the shape of galaxies. Beyond nature, however, human beings are fractal thinkers. We depend on fractal algorithms
From playlist Celebration of Mind
Fractal properties, noise-sensitivity and chaos in models of random geometry - Shirshendu Ganguly
Probability Seminar Topic: Fractal properties, noise-sensitivity and chaos in models of random geometry. Speaker: Shirshendu Ganguly Affiliation: University of California, Berkeley Date: March 31, 2023 Planar last passage percolation models are canonical examples of stochastic growth, po
From playlist Mathematics
Henry Adams (6/2/20): From persistent homology to machine learning
Title: From persistent homology to machine learning Abstract: I will give an overview of a variety of ways to turn persistent homology output into input for machine learning tasks, including a discussion of the stability and interpretability properties of these methods. Persistent homolog
From playlist SIAM Topological Image Analysis 2020
Tipping in Spatial Systems (Lecture 3) by Vishwesha Guttal
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
Disorder-generated multifractals and random matrices: freezing phenomena and extremes - Yan Fyodorov
Yan Fyodorov Queen Mary University of London October 3, 2013 I will start with discussing the relation between a class of disorder-generated multifractals and logarithmically-correlated random fields and processes. An important example of the latter is provided by the so-called "1/f noise"
From playlist Mathematics
Geometer Explains One Concept in 5 Levels of Difficulty | WIRED
Computer scientist Keenan Crane, PhD, is asked to explain fractals to 5 different people; a child, a teen, a college student, a grad student, and an expert. Still haven’t subscribed to WIRED on YouTube? ►► http://wrd.cm/15fP7B7 Listen to the Get WIRED podcast ►► https://link.chtbl.com
From playlist Tutorials and Lectures
I'm working on an engine to create 3D fractals like these, and I made a few renders I thought looked really nice. How 3D Fractals Work: https://www.youtube.com/watch?v=svLzmFuSBhk Rendered using PySpace: https://github.com/HackerPoet/PySpace Music "Perfect Fracture" by Ecko https://soun
From playlist Fractals & Math