favicon, apple ][ header and small typos

created favicon files using RealFaviconGenerator.net and added them to assets\images\. updated head\custome.html. updated main.scss to use a specific header for the Apple ][+ blog. added apple2-header.jpg. fixed typos in k-means.md.

Author: mdcramer

_apple-2-blog/k-means.md

@@ -13,19 +13,19 @@ last_modified_at: 2025-10-06
 
 Wait. Does k-means count as machine learning? Yes. Yes, it does.
 
-[CS229](https://cs229.stanford.edu/){:target="_blank"} is the graduate-level machine learning course I took at Stanford as part of the [Graduate Certificate in AI](https://www.linkedin.com/pulse/graduate-certificate-ai-achievement-unlocked-mark-cramer/){:target="_blank"} which I received back in 2021. While k-means is my choice as the easiest to understand algorithm in machine learning, it was taught as the introductory clustering algorithm for unsupervised learning. As a TA for [XCS229](https://online.stanford.edu/courses/xcs229-machine-learning){:target="_blank"}, which I have been doing since 2022 and most recently did this Spring, I know that it is still being taught as part of this seminal course in AI.
+[CS229](https://cs229.stanford.edu/){:target="_blank"} is the graduate-level machine learning course I took at Stanford as part of the [Graduate Certificate in AI](https://www.linkedin.com/pulse/graduate-certificate-ai-achievement-unlocked-mark-cramer/){:target="_blank"} which I completed in 2021. While k-means is my choice as the easiest to understand algorithm in machine learning, it was taught as the introductory clustering algorithm for unsupervised learning. As a TA for [XCS229](https://online.stanford.edu/courses/xcs229-machine-learning){:target="_blank"}, which I have been doing since 2022 and most recently did this Spring, I know that it is still being taught as part of this seminal course in AI.
 
 ## We have liftoff!
 
 Unlike [previously](/apple-2-blog/synthesizing-data/) where I saved the result for the end, let's start by taking a look at the algorithm in action!
 
 [![Video of Apple 2+ running k-means](https://img.youtube.com/vi/Cy0wMMLObVA/0.jpg)](https://youtube.com/shorts/Cy0wMMLObVA?autoplay=1 "Video of Apple ]\[+ running k-means"){:target="_blank"}
 
-Here is a screenshot of the final decision boundary after convergence.
+Here is a screenshot of the decision boundary after convergence.
 
 ![K-means decision boundary after convergence](/assets/images/apple2/k-means-convergence.jpg "K-means decision boundary after convergence")
 
-The final accuracy is 90% because 1 of the 10 observations is on the incorrect side of the decision boundary.
+Accuracy is 90% because 1 of the 10 observations is on the incorrect side of the decision boundary.
 
 For debugging purposes, to speed up execution, I reduced the number of samples in each class to 5. (You might note that, on the graph, there are only 4 points in class 1, which are the □s. That's because one of the points is at `(291, 90)`, which is off the edge of the screen. Gaussian distributions can generate extreme outliers, so I decided to preserve those points rather than clip them to the edge of the screen.) That's obviously pretty small but you can see the algorithm iterating.
 

_includes/head/custom.html

@@ -15,4 +15,12 @@
 <meta property="twitter:url" content="{{ page.url | absolute_url }}">
 <meta property="twitter:title" content="{{ page.title | default: site.title }}">
 <meta property="twitter:description" content="{{ page.excerpt | default: site.description | strip_html | truncate: 160 }}">
-<meta property="twitter:image" content="{{ page.image | default: site.og_image | absolute_url }}">
+<meta property="twitter:image" content="{{ page.image | default: site.og_image | absolute_url }}">
+
+<!-- Favicon -->
+<link rel="icon" type="image/png" href="/assets/images/favicon.ico/favicon-96x96.png" sizes="96x96" />
+<link rel="icon" type="image/svg+xml" href="/assets/images/favicon.ico/favicon.svg" />
+<link rel="shortcut icon" href="/assets/images/favicon.ico/favicon.ico" />
+<link rel="apple-touch-icon" sizes="180x180" href="/assets/images/favicon.ico/apple-touch-icon.png" />
+<meta name="apple-mobile-web-app-title" content="Hackin’ and Tinkerin’" />
+<link rel="manifest" href="/assets/images/favicon.ico/site.webmanifest" />

assets/css/main.scss

@@ -42,6 +42,13 @@
                -1px 1px 2px rgba(255,255,255,0.7) !important;
 }
 
+/* Apple 2 blog specific header */
+/* https://claude.ai/share/ea376385-c62a-4607-93a6-51cc03e81b1d */
+body.apple-2-blog .page__hero--overlay {
+  background: linear-gradient(rgba(0, 0, 0, 0.3), rgba(0, 0, 0, 0.3)), 
+              url('/assets/images/apple2-header.jpg') center top/cover no-repeat !important;
+}
+
 /* define the no-break class to prevent any line breaks within that element */
 .no-break {
   white-space: nowrap;