lpsc/fractal_project/README.md has been updated and...

lpsc/fractal_project/README.md has been updated and lpsc/fractal_project/mandelbrot.md has been added.

fractal_project/README.md

 # Mandelbrot set
 
-## What is the Mandelbrot set?
-
-## Calculation of the Mandelbrot set
-
-The **Mandelbrot set** is the set of **complex numbers** $c$ for which the function $f_{c}(z) = z^{2} + c$ does **not** diverge when iterated from $z_{0} = 0$. This means that starting with $z = 0$, if the iterations of the function $f_{c}(z) = z^{2} + c$ do not cause $\left\lvert z \right\rvert$ to grow beyond a certain threshold (usually $2$) after many iterations, then the point $c$ is part of the Mandelbrot set.
-
-### 1. Choose a complex constant $c$
-
-> * Fot the Mandelbrot set, $c$ **is the parameter** that changes with each point we check in the complex plane. The set is defined by **which value of $c$ produce bounded iterates**.
-
-### 2. Define the complex plane
-
-> * We need a grid of complex numbers $z$ to iterate over. This grid typically covers a region of the complex plane, like:
->> * Real part $x$ from $-2$ to $2$.
->> * Imaginary part $y$ from $-2$ to $2$.
-
-### 3. Start with $z_{0} = 0$
-
-> * For the Mandelbrot set, **we always start with $z = 0$** for every value of $c$. So, the iteration begins from the point $z_{0} = 0$.
-
-### 4. Iterate the function $f_{c}(z) = z^{2} + c$
-
-> * Apply the function iteratively to the value $z$ starting from $z_{0} = 0$, using the formula:
->> $f_{c}(z) = z^{2} + c$
-> * For each point $c$, we iterate and check whether $\left\lvert z_{n} \right\rvert$ (the magnitude of $z_{n}$) stays bounded (i.e., does not grow beyond a threshold like $2$).
-> * If the value of $\left\lvert z_{n} \right\rvert$ grows beyond $2$, then the point $c$ **is not** part of the Mandelbrot set (i.e., it escapes to infinity).
-
-### 5. Check if $\left\lvert z_{n} \right\rvert$ (the modulus of $z_{n}$) escapes
-
-> * **Escape condition**: If the magnitude $\left\lvert z_{n} \right\rvert$ of the current value of $z$ becomes greater than $2$, we stop iterating because the value will continue growing towards infinity. This means that the point $c$ is **not part of the Mandelbrot set**.
-> * If $\left\lvert z_{n} \right\rvert$ stays below $2$ after a certain number of iterations, then the point $c$ is considered **part of the Mandelbrot set**.
-
-### 6. Repeat the iteration for a maximum number of iterations
-
-> * The number of iterations we run is often limited to a maximum (like $100$). If the value of $z$ does not escape within that many iterations, we consider it part of the Mandelbrot set.
-
-### 7. Color the point
-
-> * Points that escape quickly (i.e., after just a few iterations) can be colored differently from those that take longer to escape.
-> * Points that do **not escape** (after the maximum number of iterations) are part of the Mandelbrot set and are typically colored black.
-
-### 8. Repeat for all points in the complex plane
-
-> * After performing these iterations for each point in the grid of complex numbers, you can plot the results.
+1. [Mandelbrot set](./mandelbrot.md)
 
 # Julia set
 
@@ -57,8 +14,8 @@ The most common function used for Julia sets is the **quadratic** function:
 
 Where:
 
-<!-- > * $c$ is a fixed complex number (a constant), chosen by you. -->
-<!-- > * $z$ is the point in the complex plane you are testing (a complex number $z=x+y$, where $x$ are real numbers). -->
+> * $c$ is a fixed complex number (a constant), chosen by you.
+> * $z$ is the point in the complex plane you are testing (a complex number $z=x+y$, where $x$ are real numbers).
 
 ## Calculation of the Julia set
 

fractal_project/mandelbrot.md

+# Mandelbrot set
+
+## What is the Mandelbrot set?
+
+## Calculation of the Mandelbrot set
+
+The **Mandelbrot set** is the set of **complex numbers** $c$ for which the function $f_{c}(z) = z^{2} + c$ does **not** diverge when iterated from $z_{0} = 0$. This means that starting with $z = 0$, if the iterations of the function $f_{c}(z) = z^{2} + c$ do not cause $\left\lvert z \right\rvert$ to grow beyond a certain threshold (usually $2$) after many iterations, then the point $c$ is part of the Mandelbrot set.
+
+### 1. Choose a complex constant $c$
+
+> * Fot the Mandelbrot set, $c$ **is the parameter** that changes with each point we check in the complex plane. The set is defined by **which value of $c$ produce bounded iterates**.
+
+### 2. Define the complex plane
+
+> * We need a grid of complex numbers $z$ to iterate over. This grid typically covers a region of the complex plane, like:
+>> * Real part $x$ from $-2$ to $2$.
+>> * Imaginary part $y$ from $-2$ to $2$.
+
+### 3. Start with $z_{0} = 0$
+
+> * For the Mandelbrot set, **we always start with $z = 0$** for every value of $c$. So, the iteration begins from the point $z_{0} = 0$.
+
+### 4. Iterate the function $f_{c}(z) = z^{2} + c$
+
+> * Apply the function iteratively to the value $z$ starting from $z_{0} = 0$, using the formula:
+>> $f_{c}(z) = z^{2} + c$
+> * For each point $c$, we iterate and check whether $\left\lvert z_{n} \right\rvert$ (the magnitude of $z_{n}$) stays bounded (i.e., does not grow beyond a threshold like $2$).
+> * If the value of $\left\lvert z_{n} \right\rvert$ grows beyond $2$, then the point $c$ **is not** part of the Mandelbrot set (i.e., it escapes to infinity).
+
+### 5. Check if $\left\lvert z_{n} \right\rvert$ (the modulus of $z_{n}$) escapes
+
+> * **Escape condition**: If the magnitude $\left\lvert z_{n} \right\rvert$ of the current value of $z$ becomes greater than $2$, we stop iterating because the value will continue growing towards infinity. This means that the point $c$ is **not part of the Mandelbrot set**.
+> * If $\left\lvert z_{n} \right\rvert$ stays below $2$ after a certain number of iterations, then the point $c$ is considered **part of the Mandelbrot set**.
+
+### 6. Repeat the iteration for a maximum number of iterations
+
+> * The number of iterations we run is often limited to a maximum (like $100$). If the value of $z$ does not escape within that many iterations, we consider it part of the Mandelbrot set.
+
+### 7. Color the point
+
+> * Points that escape quickly (i.e., after just a few iterations) can be colored differently from those that take longer to escape.
+> * Points that do **not escape** (after the maximum number of iterations) are part of the Mandelbrot set and are typically colored black.
+
+### 8. Repeat for all points in the complex plane
+
+> * After performing these iterations for each point in the grid of complex numbers, you can plot the results.