Initial commit. Tool works already :)

Makefile

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+
+fourier : main.cpp
+	$(CXX) $(CXXFLAGS) -Ofast -Wall main.cpp -o fourier

README.md

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+Fourier Transform
+=================
+
+This tool was inspired by the following comic:
+![Explanation of the Fourier transform](http://www.smbc-comics.com/comics/20130201.gif)
+
+The comic was right about 624 being the fouriest in base 5, however 625 is fouriest in both base 12 and 23! Amazing!

fourier-transform.sublime-project

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+{
+	"folders":
+	[
+		{
+			"path": "/Users/joshua/Documents/Code/fourier-transform"
+		}
+	]
+}

main.cpp

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+/*
+	Calculates the optimal fourier transform(s) for a number
+	Also outputs distribution of least-fouerist-base
+	Inspired by http://www.smbc-comics.com/?id=2874
+
+	A very naive implementation :)
+*/
+
+#include <map>
+#include <vector>
+#include <iomanip>
+#include <iostream>
+#include <algorithm>
+#include <iterator>
+
+using namespace std;
+
+int length(int number, int base){
+	int length = 1;
+	int acc = base;
+
+	while(number >= acc){
+		length++;
+		acc *= base;
+	}
+
+	return length;
+}
+
+int fours(int number, int base){
+	int count = (number % base) == 4;
+
+	while(number > base){
+		number /= base;
+		if(number % base == 4) count++;
+	}
+
+	return count;
+}
+
+// Performs a fourier transform to make the input fourier
+// Done with a linear search, there are probably betters ways
+// There is not always a unique base in which the input is fouriest, so we output a vector
+vector<int> fourier(int input){
+	int base = 1;
+	int current_best = 0;
+	vector<int> bests{};
+
+	do {
+		base++;
+		int current = fours(input, base);
+		if(current >= current_best){
+			if(current > current_best){
+				bests.clear();
+				current_best = current;
+			}
+			bests.push_back(base);
+		}
+	} while(length(input, base) > 1);
+
+	return bests;
+}
+
+// The input number is shown, then the fouriness, then the bases in which the input is fouriest.
+int main(){
+	map<int, int> distribution;
+
+	cout << "Number, \t Fouriness, \t Possible bases" << endl;
+	for(int i = 1; i < 1000; i++){
+		auto bases = fourier(i);
+		auto nfours = fours(i, bases.back());
+
+		distribution[bases.front()]++;
+
+		cout << setw(5) << i << ", \t" << setw(5) << nfours << ", \t[ ";
+		copy(begin(bases), end(bases), ostream_iterator<int>(cout, " "));
+		cout << "]" << endl;
+	}
+
+	cout << "\nDistribution of least bases" << endl;
+	for(auto x : distribution){
+		cout << x.first << ", \t" << x.second << endl;
+	}
+}