From cc1c586983a490fa556e642d57ebe50d01e2197f Mon Sep 17 00:00:00 2001
From: "joachim.schmidt" <joachim.schmidt@hesge.ch>
Date: Thu, 13 Mar 2025 11:34:13 +0100
Subject: [PATCH] fractal_project/README.md has been updated.
---
fractal_project/README.md | 12 +++++++++++-
1 file changed, 11 insertions(+), 1 deletion(-)
diff --git a/fractal_project/README.md b/fractal_project/README.md
index 587fa52..25d6600 100644
--- a/fractal_project/README.md
+++ b/fractal_project/README.md
@@ -27,14 +27,24 @@ The **Mandelbrot set** is the set of **complex numbers** $c$ for which the funct
> * 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
+### 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.
+
# Julia set
## What is a Julia set?
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GitLab