The other day I read an article about how to create fractals using the midpoint displacement algorithm. It's a simple recursive algorithm where you take a square, and split it into 4 smaller squares while displacing the height of the corner where the 4 squares join by a random amount. This process is repeated, creating smaller squares which gradually make a smoother terrain. I spent an hour or two writing a PHP script to make a terrain image using this method. After I got some decent looking greyscale images, I added a color map so I could create colored oceans and mountains. Today I modified my old 3D graph script to generate 3D terrains using a bitmap and elevation map from my new fractal Here is what it looks like: sproutworks.com/artgraph.php?bitmap=image_1296466523.jpg&elvmap=elevation_1296466523.jpg&height=200 I might work on getting a terrain generator running in the iPhone, and rendering it with OpenGL.

I have been playing with some iterated function systems again. These images were built using two affine transformations, one being a rotation through 20 degree composed a scaling of 90% and the second is a general affine transformation chosen at random. Some of the best of these results I have attached here. I have added...

Above is an image of “dry ice spiders” on Mars. Every spring the Sun warms up the Martian south polar icecap and causes jets of carbon-dioxide gas to erupt through the icecap. These jets carrying dark sand into the air and spraying it for hundreds of feet around each jet forming these wonderful spider-like structures....

Fractals are common in nature because of the surprisingly simple way they are made. Mathematically, they also help us make sense of complexity and chaos – and maybe even quantum weirdness

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.

This paper reports on the two-scale fractal structure of chromatin organization in the nucleus of the HeLa cell.

What has sometimes been described as mobile middleware has taken a new tack. Now, the idea of Backend as a Service (BaaS) has begun to take off in the mobile application development space. Proponents of BaaS say it helps developers easily build mobile apps, or any other applications connected to a cloud backend. Some of Read the rest...

M. V. Pratsiovytyi and S. P. Ratushniak
Theor. Probability and Math. Statist. 99 (2020), 211-228.
Abstract, references and article information

Outdoors, patterns abound. One need not be a mathematician in order to view and appreciate them. The widening whorls of seeds in a sunflower head are often used to illustrate the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8….) in which each figure is the sum of the two preceding digits. Other […]

The post Fractals and Flow appeared first on DNERR Blog - State of Delaware.

This chapel looks to nature and the generations-old tradition of Japanese wood joinery for inspiration.

Steeb, W.-H

New Haven : Yale University Press, [2016]

Malik, Pravir

To study the biological differences brought on by space travel, NASA sent one twin into space and kept another on Earth in 2015. Now, researchers from that project are trying to replicate that work planet-side to see whether the differences in gene expression were due to extreme stress or were specific to being in space. Sarah Crespi talks with Online News Editor Catherine Matacic about a “control” study using what might be a comparably stressful experience here on Earth: climbing Mount Everest. Catherine also shares a recent study that confirmed what one reddit user posted 5 years ago: A single path stretching from southern Pakistan to northeastern Russia will take you on the longest straight-line journey on Earth, via the ocean. Finally, Sarah talks with Roland Kröger of the University of York in the United Kingdom about his group’s study published this week in Science. Using a combination of techniques usually reserved for materials science, the group explored the nanoscale arrangement of mineral in bone, looking for an explanation of the tissue’s contradictory combination of toughness and hardness. This week’s episode was edited by Podigy. Listen to previous podcasts. [Image: Human bone (20X) by Berkshire Community College Bioscience Image Library; Music: Jeffrey Cook]

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