Imaginary Geometry
Images based on the works IG1, IG2, IG3, IG4.![](images/ig/thumbs/fan_kappa_1_4096.png)
![](images/ig/thumbs/fan_kappa_1_256.png)
![](images/ig/thumbs/fan_kappa_1_128.png)
![](images/ig/thumbs/fan_kappa_1_64.png)
![](images/ig/thumbs/fan_kappa_1_32.png)
![](images/ig/thumbs/fan_kappa_1_16.png)
![](images/ig/thumbs/fan_kappa_1_8.png)
![](images/ig/thumbs/fan_kappa_1_4.png)
![](images/ig/thumbs/fan_kappa_1_2.png)
![](images/ig/thumbs/tree_20_angle_minus_pi_4.png)
![](images/ig/thumbs/tree_20_angle_pi_4.png)
![](images/ig/thumbs/tree_20_both_pi_4_angles.png)
![](images/ig/thumbs/fans_1_2_100lines.png)
![](images/ig/thumbs/fans_1_2_100lines_b.png)
![](images/ig/thumbs/fans_1_2_100lines_c.png)
Flow lines of the Gaussian free field from the bottom to the top of the square.
![](images/ig/thumbs/simulation_0.png)
![](images/ig/thumbs/simulation_1.png)
![](images/ig/thumbs/simulation_2.png)
![](images/ig/thumbs/simulation_3.png)
![](images/ig/thumbs/simulation_4.png)
![](images/ig/thumbs/simulation_9.png)
Light cone construction of an SLE_k with k=16/3 using flow lines of the Gaussian free field
![](images/ig/thumbs/rays_4096_depth_0.png)
![](images/ig/thumbs/rays_4096_depth_1.png)
![](images/ig/thumbs/rays_4096_depth_2.png)
![](images/ig/thumbs/rays_4096_depth_3.png)
![](images/ig/thumbs/rays_4096_depth_4.png)
![](images/ig/thumbs/rays_4096.png)
Light cone construction of an SLE_k with k=64 using flow lines of the Gaussian free field. The rho values of the curve are chosen so that it only hits the domain boundary at its initial and terminal points.
![](images/ig/thumbs/sle6_orange.png)
![](images/ig/thumbs/sle6_and_sle_8_3_fan.png)
![](images/ig/thumbs/sle_sunrise2.png)
![](images/ig/thumbs/sunrise_reversible_thickness3.png)
![](images/ig/thumbs/sle_sunrise_spirals_small.png)
![](images/ig/thumbs/spiral_white.png)
![](images/ig/thumbs/spiral_white_fan.png)
![](images/ig/thumbs/sle_sunrise_colors_large.png)
![](images/ig/thumbs/sle8.png)
![](images/ig/thumbs/sle16.png)
![](images/ig/thumbs/rays_4096.png)
![](images/ig/thumbs/rays_fan_4096.png)
SLE_k type curves with k > 4 generated as light cones of SLE_(16/k) type curves coupled together as flow lines of the Gaussian free field. Animations of SLE_128 and the reversible version of SLE_128.
![](images/ig/thumbs/flowline_animation0000000025.png)
![](images/ig/thumbs/flowline_animation0000000050.png)
![](images/ig/thumbs/flowline_animation0000000075.png)
![](images/ig/thumbs/flowline_animation0000000100.png)
Space filling SLE_k with k=6. Related animation.