첨부 소스 코드는 나눔고딕코딩 폰트를 사용합니다.
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TestProject.zip
다운로드

▶ MainForm.cs

using System;
using System.Drawing;
using System.Windows.Forms;

namespace TestProject
{
    /// <summary>
    /// 메인 폼
    /// </summary>
    public partial class MainForm : Form
    {
        //////////////////////////////////////////////////////////////////////////////////////////////////// Field
        ////////////////////////////////////////////////////////////////////////////////////////// Private

        #region Field

        /// <summary>
        /// 확률 배열
        /// </summary>
        private float[] probabilityArray = { 0.01f, 0.85f, 0.08f, 0.06f };

        /// <summary>
        /// 함수 배열
        /// </summary>
        private float[, ,] functionArray =
        {
            {
                { 0, 0     },
                { 0, 0.16f },
            },
            {
                {  0.85f, 0.04f },
                { -0.04f, 0.85f },
            },
            {
                { 0.2f , -0.26f },
                { 0.23f,  0.22f },
            },
            {
                { -0.15f, 0.28f },
                {  0.26f, 0.24f },
            }
        };

        /// <summary>
        /// 플러스 배열
        /// </summary>
        private float[,] plusArray =
        {
            {0, 0     },
            {0, 1.6f  },
            {0, 1.6f  },
            {0, 0.44f },
        };

        #endregion

        //////////////////////////////////////////////////////////////////////////////////////////////////// Constructor
        ////////////////////////////////////////////////////////////////////////////////////////// Public

        #region 생성자 - MainForm()

        /// <summary>
        /// 생성자
        /// </summary>
        public MainForm()
        {
            InitializeComponent();

            #region 이벤트를 설정한다.

            Load                         += Form_Load;
            this.canvasPictureBox.Resize += canvasPictureBox_Resize;

            #endregion
        }

        #endregion

        //////////////////////////////////////////////////////////////////////////////////////////////////// Method
        ////////////////////////////////////////////////////////////////////////////////////////// Private
        //////////////////////////////////////////////////////////////////////////////// Event

        #region 폼 로드시 처리하기 - Form_Load(sender, e)

        /// <summary>
        /// 폼 로드시 처리하기
        /// </summary>
        /// <param name="sender">이벤트 발생자</param>
        /// <param name="e">이벤트 인자</param>
        private void Form_Load(object sender, EventArgs e)
        {
            DrawBarnsleyFernFractal();
        }

        #endregion
        #region 캔버스 픽처 박스 크기 조정시 처리하기 - canvasPictureBox_Resize(sender, e)

        /// <summary>
        /// 캔버스 픽처 박스 크기 조정시 처리하기
        /// </summary>
        /// <param name="sender">이벤트 발생자</param>
        /// <param name="e">이벤트 인자</param>
        private void canvasPictureBox_Resize(object sender, EventArgs e)
        {
            DrawBarnsleyFernFractal();
        }

        #endregion

        //////////////////////////////////////////////////////////////////////////////// Function

        #region 반즐리 고사리 프랙탈 그리기 - DrawBarnsleyFernFractal()

        /// <summary>
        /// 반즐리 고사리 프랙탈 그리기
        /// </summary>
        private void DrawBarnsleyFernFractal()
        {
            int imageWidth  = this.canvasPictureBox.ClientSize.Width;
            int imageHeight = this.canvasPictureBox.ClientSize.Height;

            Bitmap bitmap = new Bitmap(imageWidth, imageHeight);

            using(Graphics graphics = Graphics.FromImage(bitmap))
            {
                graphics.Clear(Color.Black);

                Random random = new Random();

                int   functionValue = 0;
                int   xIndex;
                int   yIndex;
                float x = 1;
                float y = 1;
                float x1;
                float y1;

                for(int i = 1; i <= 100000; i++)
                {
                    double randomValue = random.NextDouble();

                    for(int j = 0; j <= 3; j++)
                    {
                        randomValue = randomValue - probabilityArray[j];

                        if(randomValue <= 0)
                        {
                            functionValue = j;

                            break;
                        }
                    }

                    x1 = x * functionArray[functionValue, 0, 0] + y * functionArray[functionValue, 0, 1] + plusArray[functionValue, 0];
                    y1 = x * functionArray[functionValue, 1, 0] + y * functionArray[functionValue, 1, 1] + plusArray[functionValue, 1];

                    x = x1;
                    y = y1;

                    const float xMinimum = -4;
                    const float xMaximum = 4;
                    const float yMinimum = -0.1f;
                    const float yMaximum = 10.1f;
                    const float width    = xMaximum - xMinimum;
                    const float height   = yMaximum - yMinimum;

                    xIndex = (int)Math.Round((x - xMinimum) / width * this.canvasPictureBox.ClientSize.Width);
                    yIndex = (int)Math.Round((this.canvasPictureBox.ClientSize.Height - 1) - (y - yMinimum) / height * imageHeight);

                    if((xIndex >= 0) && (yIndex >= 0) && (xIndex < imageWidth) && (yIndex < imageHeight))
                    {
                        bitmap.SetPixel(xIndex, yIndex, Color.Lime);
                    }
                }
            }

            this.canvasPictureBox.BackgroundImage = bitmap;
        }

        #endregion
    }
}
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