Snail Sudoku (Daily Sudoku League #74)

It was the year 2004 when the first time I participated in World Puzzle Championship in Croatia. My second World Puzzle Championship was at Eger, Hungry in the year 2005, and there I took part in 24Hr Puzzle Championship. After participating in this Championship, I got motivated to create puzzles and since then I have been creating puzzles. In fact, later twice I contributed to 24Hr Championship. One time along with my Indian friends and one time I created one full set alone. Most of the puzzles created by me are published in this blog and there are many which are still on paper without any computer images. Sometimes back I found one of my notebooks where there were some of my puzzles were created around 4 years back. Today I am posting one of that puzzle Snail Sudoku in The League of Extraordinary Ladies and Gentlemen. In fact, Snail Sudoku appeared as a puzzle type in Oğuz Atay Puzzle Contest (OAPC)-2 championship and then subsequently in The Last Sudoku Competition Before World Sudoku Championship (TLSCBWSC-1). That time Snail Sudoku become on favorite puzzle type as it was like solving 9 different small interrelated puzzles.
After getting feedback on my recent contributions, I am learning Art of Creating Puzzles and Sudoku with symmetry and theme. Earlier I never used to care about these aspects of puzzle creations. In my next few contributions to The League of Extraordinary Ladies and Gentlemen, I will be submitting some of my older created puzzles. Many of these puzzles don't follow symmetry and them. Do pardon me for missing these aspects in forthcoming puzzles. These puzzles will help me to re-introduce some of the forgotten Sudoku types.
This Snail Sudoku is my 74th contribution to The League of Extraordinary Ladies and Gentlemen. Can you solve this interesting Snail Sudoku puzzle?

Rules of Snail Sudoku

Fill the grid with digits 1~4, so that each digit appears exactly once in every row, column, and every 3x3 spiral. Digits should be placed orderly in the spirals, from the entrance to the center. The numbers outside the grid indicate the first seen number from that direction.