Create cantor set.jl

Author: je-suis-tm

cantor set.jl

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+
+# coding: utf-8
+
+# In[1]:
+
+
+#fractal is one of the interesting topics in geometry
+#it is usually described by a recursive function
+#voila,here we are!
+using Plots
+
+
+# In[2]:
+
+
+#initialize
+x1=0
+x2=3
+y=0
+bar_height=5
+between_interval=10
+n=6;
+
+
+# In[3]:
+
+
+#create rectangle shape
+rectangle(w,h,x,y)=Shape(x.+[0,w,w,0],y.-[0,0,h,h])
+
+
+# In[4]:
+
+
+#cantor set is one of the simplest fractal shape
+#at each iteration,we divide each bar into three equal parts 
+#we remove the mid part from each bar and keep the rest
+#this effectively creates a binary tree
+#check the link below for more details on math
+# https//www.math.stonybrook.edu/~scott/Book331/Cantor_sets.html
+function cantor_set(x1,x2,y,n,
+               bar_height=5,between_interval=10)
+    
+    #base case
+    if n==0
+        return
+    
+    else
+        
+        #viz the first 1/3 and the last 1/3 
+        plot!(rectangle((x2-x1)/3,bar_height,x1,y-between_interval))
+        plot!(rectangle((x2-x1)/3,bar_height,x2-(x2-x1)/3,y-between_interval))
+
+        #recursion
+        cantor_set(x1,x1+(x2-x1)/3,
+                   y-between_interval,
+                   n-1)        
+        cantor_set(x2-(x2-x1)/3,x2,
+                   y-between_interval,
+                   n-1)
+        
+    end
+    
+end
+
+
+# In[5]:
+
+
+#viz
+#as n increases
+#the bar gets too slim to be visible
+fig=plot(legend=false,grid=false,axis=false,ticks=false)
+plot!(rectangle((x2-x1),bar_height,x1,y))
+cantor_set(x1,x2,y,n)
+fig
+
+