diff --git a/contents/IFS/IFS.md b/contents/IFS/IFS.md index 8ba1fb10c..15c114211 100644 --- a/contents/IFS/IFS.md +++ b/contents/IFS/IFS.md @@ -20,8 +20,8 @@ To begin the discussion of Iterated Function Systems (IFSs), we will first discu Sierpinsky Triangle Chaos Game This image is clearly a set of triangles embedded in a larger triangle in such a way that it can be continually cut into three identical pieces and still retain its internal structure. -This idea is known as self-similarity {{"self-similar" | cite }}, and it is usually the first aspect of fractals to catch an audience's attention. -In fact, there are plenty of uses of fractals and their mathematical underpinnings, such as estimating the coastline of Britain {{ "mandelbrot1967long" | cite}}, identifying fingerprints {{ "jampour2010new" | cite }}, and image compression {{ "fractal-compression" | cite }}{{ "saupe1994review" | cite }}. +This idea is known as self-similarity {{ "self-similar" | cite }}, and it is usually the first aspect of fractals to catch an audience's attention. +In fact, there are plenty of uses of fractals and their mathematical underpinnings, such as estimating the coastline of Britain {{ "mandelbrot1967long" | cite }}, identifying fingerprints {{ "jampour2010new" | cite }}, and image compression {{ "fractal-compression" | cite }}{{ "saupe1994review" | cite }}. In many more rigorous definitions, a fractal can be described as any system that has a non-integer Hausdorff dimension {{ "3b1bfractal" | cite }}{{ "hausdorff" | cite }}{{ "gneiting2012estimators" | cite }}. Though this is an incredibly interesting concept, the discussion of this chapter will instead focus on methods to generate fractal patterns through iterated function systems. @@ -41,7 +41,7 @@ f_3(P) &= \frac{P + C}{2}\\ $$ Each function will read in a particular location in space (here, $$P \in \mathbb{R}^2$$) and output a new location that is the midpoint between the input location and $$A$$, $$B$$, or $$C$$ for $$f_1$$, $$f_2$$, and $$f_3$$ respectively. -The union of all of these functions (the set of all possible functions available for use) is often notated as the _Hutchinson operator_ {{ "hutchinson-operator" | cite }}{{ "hutchinson1981fractals" | cite}}, and for this case it would look like this: +The union of all of these functions (the set of all possible functions available for use) is often notated as the _Hutchinson operator_ {{ "hutchinson-operator" | cite }}{{ "hutchinson1981fractals" | cite }}, and for this case it would look like this: $$ H(P) = \bigcup_{i=1}^3f_i(P) diff --git a/contents/stacks_and_queues/stacks_and_queues.md b/contents/stacks_and_queues/stacks_and_queues.md index e72857b96..b695f53bd 100644 --- a/contents/stacks_and_queues/stacks_and_queues.md +++ b/contents/stacks_and_queues/stacks_and_queues.md @@ -19,10 +19,9 @@ Here is a simple implementation of a stack: {% sample lang="ts" %} [import, lang:"typescript"](code/typescript/stack.ts) {% sample lang="java" %} -[import, lang:"java"](code/java/Stack.java) +[import, lang:"java"](code/java/StackTest.java) {% sample lang = "cpp"%} [import, lang:"cpp"](code/cpp/stack.cpp) -[import, lang:"java"](code/java/StackTest.java) {% sample lang="rust" %} [import, lang:"rust"](code/rust/Stack.rs) {% endmethod %} @@ -32,10 +31,9 @@ Here is a simple implementation of a queue: {% sample lang="ts" %} [import, lang:"typescript"](code/typescript/queue.ts) {% sample lang="java" %} -[import, lang:"java" ](code/java/Queue.java) +[import, lang:"java" ](code/java/QueueTest.java) {% sample lang = "cpp"%} [import, lang:"cpp"](code/cpp/queue.cpp) -[import, lang:"java" ](code/java/QueueTest.java) {% sample lang="rust" %} [import, lang:"rust" ](code/rust/Queue.rs) {% endmethod %}