more perturbing

Author: jeffwack

parameters/perturb.jl

@@ -0,0 +1,52 @@
+using GLMakie
+include("MandelbrotSet.jl")
+
+function newtriple(X,(A,B,C))
+    newA = 2*X*A+1
+    newB = 2*X*B + A^2
+    newC = 2*X*C + 2*A*B
+    return (newA,newB,newC)
+end
+
+function coefs(X)
+    list = []
+    (A,B,C) = (1,0,0)
+    for x in X
+        push!(list,(A,B,C))
+        (A,B,C) = newtriple(x,(A,B,C))
+    end
+    push!(list,(A,B,C))
+    return list
+end
+
+function perturb(X,coefs,delta)
+    delta2 = delta^2
+    delta3 = delta^3
+    for (ii,x) in enumerate(zip(X,coefs))
+        (A,B,C) = x[2]
+        Y = x[1]+delta*A + delta2*B + delta3*C
+        if abs2(Y)>4
+            return (ii,Y)
+        end
+    end
+    return (NaN,Y)
+end
+
+pilot = [0.0+1.0im]
+for ii in 1:100
+    push!(pilot,pilot[end]^2+pilot[1])
+end
+
+C = coefs(pilot)
+
+rightcenterdelta = 0.00001+0.000001im
+
+patch = julia_patch(0.0+0.0im,rightcenterdelta)
+
+PA = [(pilot,C,delta) for delta in patch]
+
+results = [perturb(stuff...) for stuff in PA]
+
+pic = [x[1] for x in results]
+
+heatmap(pic,nan_color = RGBAf(0,0,0,1),colormap = :PRGn_9)