Merge pull request #69 from fverdugo/2025-26

Rephrase exercise 3 in notebook julia_basics

docs/src/solutions_for_all_notebooks.md

@@ -27,12 +27,17 @@ ex2(f,g) = x -> f(x) + g(x)
 ### Exercise 3
 
 ```julia
-using GLMakie
-max_iters = 100
 n = 1000
 x = LinRange(-1.7,0.7,n)
 y = LinRange(-1.2,1.2,n)
-heatmap(x,y,(i,j)->mandel(i,j,max_iters))
+values = zeros(n,n)
+for j in 1:n
+    for i in 1:n
+        values[i,j] = surprise(x[i],y[j])
+    end
+end
+using GLMakie
+heatmap(x,y,values)
 ```
 
 ## Asynchronous programming in Julia

notebooks/julia_basics.ipynb

@@ -1680,7 +1680,7 @@
    "source": [
     "### Exercise 3 (hard)\n",
     "\n",
-    "Function `mandel` estimates if a given point `(x,y)` in the complex plane belongs to the [Mandelbrot set](https://en.wikipedia.org/wiki/Mandelbrot_set)."
+    "Function `surprise(x,y)` takes the `x` and `y` coordinates of a point and returns a scalar value. Visualize the result of function `surprise(x,y)` for all points in a Cartesian grid of the box with range $(-1.7,0.7)$ in the horizontal direction and range $(-1.2,1.2)$ in vertical direction. Use at least `n=1000` points in each direction (1000$^2$ points in total). What do you see? Surprise!\n"
    ]
   },
   {
@@ -1690,7 +1690,11 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "function mandel(x,y,max_iters)\n",
+    "function surprise(x,y)\n",
+    "    # You don't need to understand\n",
+    "    # the body of this function.\n",
+    "    # Treat it as a black box.\n",
+    "    max_iters = 100\n",
     "    z = Complex(x,y)\n",
     "    c = z\n",
     "    threshold=2\n",
@@ -1700,22 +1704,38 @@
     "        end\n",
     "        z = z^2 +c\n",
     "    end\n",
-    "    max_iters\n",
+    "    return max_iters\n",
     "end"
    ]
   },
   {
+   "attachments": {
+    "Screenshot%20from%202025-09-05%2014-41-15.png": {
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truncated
+    }
+   },
    "cell_type": "markdown",
-   "id": "86ea2591",
+   "id": "de548741",
    "metadata": {},
    "source": [
-    "If the value of `mandel` is less than `max_iters`, the point is provably outside the Mandelbrot set. If `mandel` is equal to  `max_iters`, then the point is provably inside the set. The larger `max_iters`, the better the quality of the estimate (the nicer will be your plot).\n",
+    "The gid of points is shown in the next figure for `n=7` (but you should use at least `n=1000`).\n",
     "\n",
-    "Plot the value of function `mandel` for each pixel in a 2D grid of the box.\n",
+    "<div>\n",
+    "<img src=\"attachment:Screenshot%20from%202025-09-05%2014-41-15.png\", width=\"550\">\n",
+    "</div>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "95e81488",
+   "metadata": {},
+   "source": [
+    "### Hints\n",
     "\n",
-    "$$(-1.7,0.7)\\times(-1.2,1.2).$$\n",
+    "* Create a matrix `values` of the right size and fill it in so that `values[i,j]=surprise(x[i],y[j])` is the value for point `i` in the horizontal direction and `j` in the vertical direction (see the figure above).\n",
-    "\n",
+    "* The vectors `x` and `y` can be created with function `LinRange`.\n",
-    "Use a grid resolution of at least 1000 points in each direction and `max_iters` at least 10. You can increase these values to get nicer plots. To plot the values use function `heatmap` from the Julia package `GLMakie`. Use `LinRange` to divide the horizontal and vertical axes into pixels. See the documentation of these functions for help. `GLMakie` is a GPU-accelerated plotting back-end for Julia. It is a large package and it can take some time to install and to generate the first plot. Be patient."
+    "* Visualize the values in `values` with function `heatmap` from the Julia package `GLMakie`. `GLMakie` is a GPU-accelerated plotting back-end for Julia. It is a large package and it can take some time to install and to generate the first plot. Be patient.\n",
+    "*  See the documentation of these functions for help."
    ]
   },
   {