Update ReadMe and tweak posts

rosslh · rosslh · commit 3dcf63a14fbf · 2025-09-01T09:40:44.000-04:00
diff --git a/README.md b/README.md
@@ -17,35 +17,36 @@
   <img src="https://img.shields.io/badge/License-MIT-blue?style=flat" alt="MIT license">
 </p>
 
+<p align="center">
+  As seen in:
+  <a href="https://news.ycombinator.com/item?id=43375676">Hacker News</a> •
+  <a href="https://www.creativemachine.io/cm-tam/educational-art/benoit-mandelbrot">Creative Machine</a> •
+  <a href="https://www.sciencenews.org/article/fractals-math-science-society-50-years"><em>Science News</em> magazine</a>
+</p>
+
 ## Features
 
-Mandelbrot.site offers a variety of features to enhance your experience:
+Mandelbrot.site allows you to discover the Mandelbrot set through intuitive **zoom controls** using scrolling or region selection, while **viewport coordinates** continuously track your position on the complex plane.
 
-- **Zoom in** by scrolling or selecting a region.
-- Adjust the **detail level** by modifying the iteration count or resolution.
-- Download **high-resolution images** of your current view.
-- Generate URLs to **share** your favorite Mandelbrot set locations.
-- Customize your experience with different **color palettes**.
-- Explore **multibrot sets** by changing the exponent parameter.
-- View and update **viewport coordinates** on the complex plane.
+The visualization experience can be customized by adjusting the **iteration count** or **resolution** settings for varying levels of detail, switching between **color palettes** to reveal different structures, and even exploring **multibrot sets** by changing the exponent parameter.
+
+Beyond exploration, this web app allows you to share discoveries with high-resolution **image downloads** and **shareable URLs** that preserve exact locations and zoom levels, enabling others to access and experience the fractal views you found.
 
 ## Gallery
 
-Explore some stunning images generated with Mandelbrot.site:
+Example images generated with Mandelbrot.site:
 
 <img src="https://raw.githubusercontent.com/rosslh/mandelbrot.site/main/example-images/mandelbrot-01.png" height="200px" alt="Mandelbrot Example 1"> <img src="https://raw.githubusercontent.com/rosslh/mandelbrot.site/main/example-images/mandelbrot-02.png" height="200px" alt="Mandelbrot Example 2">
 
 [View more images](/example-images)
 
 ## Architecture
 
-Mandelbrot.site is built using modern web technologies to deliver a high-performance, interactive tool for exploring fractals. The computational backend is implemented in [Rust](https://github.com/rust-lang/rust), chosen for its performance and safety features. This Rust code is compiled to [WebAssembly](https://webassembly.org/) (Wasm) using the [wasm-pack](https://github.com/rustwasm/wasm-pack) plugin, enabling high-speed computations directly in the browser. On the frontend, the user interface is crafted with [TypeScript](https://github.com/microsoft/TypeScript), enhancing code quality and maintainability. [Leaflet.js](https://github.com/Leaflet/Leaflet) is creatively adapted to render the Mandelbrot set tiles in a zoomable, map-like interface.
-
-For performance optimization, it employs [Web Workers](https://developer.mozilla.org/en-US/docs/Web/API/Web_Workers_API) via the [threads.js](https://github.com/andywer/threads.js) library. This setup prevents intensive computations from blocking the main browser thread by creating a pool of workers that handle the generation of Mandelbrot set tiles in parallel. A key optimization technique used is "rectangle checking," which saves computation time for areas entirely within the set by checking only the perimeter of a tile.
+Mandelbrot.site uses a WebAssembly-based architecture for high-performance fractal computation in the browser. The computational backend is implemented in [Rust](https://github.com/rust-lang/rust) for performance and safety. This Rust code is compiled to [WebAssembly](https://webassembly.org/) (Wasm) using the [wasm-pack](https://github.com/rustwasm/wasm-pack) plugin, allowing fast computations directly in the browser. The frontend uses [TypeScript](https://github.com/microsoft/TypeScript) for type safety and [Leaflet.js](https://github.com/Leaflet/Leaflet) to render the Mandelbrot set tiles in a zoomable, map-like interface.
 
-It is a [Progressive Web App](https://developer.mozilla.org/en-US/docs/Web/Progressive_web_apps) (PWA), leveraging [Service Workers](https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API) to prioritize a local-first experience. This ensures that users can explore the Mandelbrot set with minimal network dependencies.
+Performance is optimized using [Web Workers](https://developer.mozilla.org/en-US/docs/Web/API/Web_Workers_API) via the [threads.js](https://github.com/andywer/threads.js) library. This prevents computations from blocking the main browser thread by creating a pool of workers that generate Mandelbrot set tiles in parallel. The "rectangle checking" optimization reduces computation time for areas entirely within the set by checking only the perimeter of a tile.
 
-This robust architecture allows Mandelbrot.site to provide a seamless and responsive experience for users exploring the intricate details of the Mandelbrot set through an online interface.
+The site is a [Progressive Web App](https://developer.mozilla.org/en-US/docs/Web/Progressive_web_apps) (PWA), using [Service Workers](https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API) for offline functionality and reduced network dependencies.
 
 ## Development
 
@@ -55,8 +56,6 @@ A complete guide can be found in [CONTRIBUTING.md](CONTRIBUTING.md#your-first-co
 
 ## Contributors
 
-Many thanks to the following contributors who have helped shape this project:
-
 |                                                                                                                    | Name                     | GitHub Profile                                                              |
 | ------------------------------------------------------------------------------------------------------------------ | ------------------------ | --------------------------------------------------------------------------- |
 | <img src="https://avatars.githubusercontent.com/u/8635605?v=4" width="50" height="50" alt="Ross Hill">             | **Ross Hill**            | [rosslh](https://github.com/rosslh)                                         |
diff --git a/client/blog/history-of-mandelbrot-set.md b/client/blog/history-of-mandelbrot-set.md
@@ -11,7 +11,7 @@ The set itself is defined by a simple iterative process. For each point `c` in t
 
 Benoit Mandelbrot, while working at IBM in the 1970s and 1980s, used the company's powerful computers to visualize this iterative process. The resulting images, which depicted the boundary of the Mandelbrot set, were unlike anything seen before. The intricate, swirling patterns and the set's apparent self-similarity at various scales were both beautiful and perplexing. The images quickly gained popularity, and the Mandelbrot set became a symbol of the emerging field of fractal geometry.
 
-Mathematically, the Mandelbrot set has several interesting properties. It is a connected set, meaning that any two points within the set can be joined by a path that lies entirely within the set. The set is also self-similar, exhibiting similar patterns at increasingly smaller scales. This property is characteristic of fractals, a term coined by Mandelbrot himself. The boundary of the Mandelbrot set is believed to have a Hausdorff dimension around 2, which highlights its intricate complexity that exceeds that of a simple curve.
+Mathematically, the Mandelbrot set has several interesting properties. It is a connected set, meaning that any two points within the set can be joined by a path that lies entirely within the set. The set is also self-similar, exhibiting similar patterns at increasingly smaller scales. This property is characteristic of fractals, a term coined by Mandelbrot himself. The boundary of the Mandelbrot set has a Hausdorff dimension of exactly 2, as proven by Shishikura in 1994, which highlights its intricate complexity that exceeds that of a simple curve.
 
 The Mandelbrot set is closely related to another class of fractals called Julia sets, where each point `c` in the complex plane corresponds to a Julia set defined by the iteration `z=z^2+c`. Julia sets associated with points inside the Mandelbrot set are connected, whereas those associated with points outside are typically disconnected. The Mandelbrot set can be thought of as a "map" of all Julia sets, with each point in the Mandelbrot set corresponding to a unique Julia set.
 
diff --git a/client/blog/what-is-mandelbrot-set.md b/client/blog/what-is-mandelbrot-set.md
@@ -13,7 +13,7 @@ Visually, the Mandelbrot Set is often represented as a black and white or colorf
 
 One of the most remarkable properties of the Mandelbrot Set is its fractal nature. Fractals are geometric objects that exhibit self-similarity at different scales, meaning that smaller portions of the object resemble the whole. The Mandelbrot Set is a prime example of a fractal, as its boundary contains an infinite number of smaller copies of the entire set, each with its own unique variations and details. This property of infinite complexity has made the Mandelbrot Set a subject of intense study and fascination among mathematicians and computer scientists.
 
-Another notable characteristic of the Mandelbrot Set is its connectedness. Despite its incredibly intricate boundary, the Mandelbrot Set is a connected set, meaning that any two points within the set can be connected by a path that lies entirely within the set. This property was proven mathematically in the early 1980s and has since been the subject of further research and generalization.
+Another notable characteristic of the Mandelbrot Set is its connectedness. Despite its incredibly intricate boundary, the Mandelbrot Set is a connected set, meaning that any two points within the set can be connected by a path that lies entirely within the set. This property was proven mathematically in 1985 by Douady and Hubbard and has since been the subject of further research and generalization.
 
 The discovery of the Mandelbrot Set has had far-reaching implications across various fields. In mathematics, it has become a cornerstone of fractal geometry and chaos theory, providing a rich playground for the study of complex dynamics and iterative behaviors. In the realm of art and design, the Mandelbrot Set has inspired countless digital and traditional artworks, captivating audiences with its mesmerizing beauty and intricate patterns. The set has also found practical applications in fields as diverse as physics, biology, and computer graphics. For instance, in physics, it offers a model for understanding turbulent systems and patterns at cosmic scales. In biology, it helps visualize and analyze patterns similar to those found in natural growth processes, such as the branching of trees or the structures of vascular systems. In computer graphics, fractal algorithms inspired by the Mandelbrot Set enable the creation of detailed, realistic landscapes and textures, enriching both video games and animated films.
 
diff --git a/client/blog/who-was-benoit-mandelbrot.md b/client/blog/who-was-benoit-mandelbrot.md
@@ -5,14 +5,14 @@ excerpt: Dive into the life and work of Benoit Mandelbrot, the pioneering mathem
 
 Benoit Mandelbrot, a Polish-born French-American mathematician, is widely recognized as the father of fractal geometry. His groundbreaking work revolutionized our understanding of complex systems and has had a profound impact on fields ranging from mathematics and physics to economics and art.
 
-Born in Warsaw, Poland, in 1924, Mandelbrot grew up in a family that valued education and intellectual pursuits. His parents, both highly educated, encouraged his curiosity and love for mathematics from an early age. Mandelbrot's family moved to France in 1936, where he continued his education, ultimately earning degrees in mathematics from universities in Paris and the United States.
+Born in Warsaw, Poland, in 1924, Mandelbrot grew up in a family that valued education and intellectual pursuits. His mother was a dental surgeon and his father was in the clothing business. They encouraged his curiosity and love for mathematics from an early age. Mandelbrot's family moved to France in 1936, where he continued his education, ultimately earning degrees in mathematics from universities in Paris and the United States.
 
 Mandelbrot's career took off when he joined IBM as a researcher in 1958. It was during his time at IBM that he began to develop the concepts that would later become known as fractal geometry. Fractals are complex geometric shapes that exhibit self-similarity at various scales. Mandelbrot discovered that many natural phenomena, such as coastlines, mountains, and even financial markets, could be described using fractal geometry.
 
-In 1975, Mandelbrot published his seminal work, "Les Objets Fractals: Forme, Hasard et Dimension," which was later translated into English as "The Fractal Geometry of Nature." This book introduced the world to the beauty and complexity of fractals and demonstrated their applicability across a wide range of disciplines. Mandelbrot's work helped to bridge the gap between mathematics and the natural world, showing that seemingly chaotic and irregular patterns could be described using simple mathematical rules.
+In 1975, Mandelbrot published his seminal work, "Les Objets Fractals: Forme, Hasard et Dimension," which was translated into English as "Fractals: Form, Chance and Dimension" in 1977. He later published his more comprehensive work "The Fractal Geometry of Nature" in 1982. These books introduced the world to the beauty and complexity of fractals and demonstrated their applicability across a wide range of disciplines. Mandelbrot's work helped to bridge the gap between mathematics and the natural world, showing that seemingly chaotic and irregular patterns could be described using simple mathematical rules.
 
-Mandelbrot's contributions to mathematics and science have had a lasting impact. His ideas have been applied to fields as diverse as computer graphics, geology, medicine, and economics.
+Mandelbrot's contributions to mathematics and science have had a lasting impact. His fractal geometry concepts have been applied to fields as diverse as computer graphics and economics, while fractal patterns are studied in geology and medicine for understanding natural phenomena.
 
-Throughout his career, Mandelbrot received numerous awards and honors, including the Wolf Prize in Physics and the Japan Prize. He was also elected to the National Academy of Sciences and the French Academy of Sciences. Mandelbrot's work continues to inspire and influence researchers and thinkers across the globe, and his legacy as a visionary mathematician and scientist is secure.
+Throughout his career, Mandelbrot received numerous awards and honors, including the Wolf Prize in Physics and the Japan Prize. He was elected to the National Academy of Sciences. Mandelbrot's work continues to inspire and influence researchers and thinkers across the globe, and his legacy as a visionary mathematician and scientist is secure.
 
-In conclusion, Benoit Mandelbrot was a pioneering mathematician whose work on fractal geometry has had a profound and lasting impact on our understanding of the world around us. His insights into the nature of complexity and irregularity have transformed the way we approach problems in mathematics, science, and beyond. Mandelbrot's legacy serves as a testament to the power of intellectual curiosity and the importance of interdisciplinary thinking in pushing the boundaries of human knowledge.
+Mandelbrot passed away on October 14, 2010, at age 85 from pancreatic cancer. He was a pioneering mathematician whose work on fractal geometry has had a profound and lasting impact on our understanding of the world around us. His insights into the nature of complexity and irregularity have transformed the way we approach problems in mathematics, science, and beyond. Mandelbrot's legacy serves as a testament to the power of intellectual curiosity and the importance of interdisciplinary thinking in pushing the boundaries of human knowledge.
