From 5065f00d6d82c396cb6a9c30cb054b86f3ed0bc5 Mon Sep 17 00:00:00 2001
From: "joachim.schmidt" <joachim.schmidt@hesge.ch>
Date: Thu, 13 Mar 2025 11:25:04 +0100
Subject: [PATCH] fractal_project/README.md has been updated.

---
 fractal_project/README.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/fractal_project/README.md b/fractal_project/README.md
index fba577f..587fa52 100644
--- a/fractal_project/README.md
+++ b/fractal_project/README.md
@@ -12,10 +12,21 @@ The **Mandelbrot set** is the set of **complex numbers** $c$ for which the funct
 
 ### 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 $\left\lvert z \right\rvert$ (the modulus of $z$) escapes
 
 ### 6. Repeat the iteration for a maximum number of iterations
-- 
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